Bartleby Sitemap - Textbook Solutions
All Textbook Solutions for Mathematical Excursions (MindTap Course List)
45ESGiven that my=130, find the measures of angles a and b.47ES48ES49ES50ES51ES52ES53ESCut out a triangle and then tear off two of the angles, as shown below. Position angle a so that it is to the left of angle b and is adjacent to angle b. Now position angle c so that it is to the right of angle b and is adjacent to angle b. Describe what you observe. What does this demonstrate?55ES56ESIf AB and CD intersect at point O, and mAOC=mBOC, explain why ABCD.Complete the table below by calculating the length, width, perimeter, and area of the rectangle after the given number of seconds have elapsed.2EE3EE4EE5EE6EEWhat is wrong with each statement? a. The perimeter is 40 m2. b. The area is 120 ft.2ES3ES4ES5ESFind (a ) the perimeter and (b ) the area of the figure.7ES8ES9ES10ES11ESFind (a ) the circumference and (b ) the area of the figure. State an exact answer and a decimal approximation rounded to the nearest hundredth.13ES14ES15ES16ESCross-Country A cross-country course is in the shape of a parallelogram with a base of length 3 mi and a side of length 2 mi. What is the total length of the cross-country course?18ESSewing Bias binding is to be sewn around the edge of a rectangular tablecloth measuring 68 in. by 42 in. If the bias binding comes in packages containing 15 ft of binding, how many packages of bias binding are needed for the tablecloth?20ES21ES22ES23ESAthletic Fields Artificial turf is being used to cover a playing field. If the field is rectangular with a length of 110 yd and a width of 80 yd. how much artificial turf must be purchased to cover the field?25ES26ESArea The width of a rectangle is 8 ft. If the area is 312 ft2, what is the length of the rectangle?Area The area of a parallelogram is 56 m2. If the height of the parallelogram is 7 m, what is the length of the base?29ESSailing A sail is in the shape of a triangle with a base of 12 m and a height of 16 m. How much canvas was needed to make the body of the sail?Gardens A vegetable garden is in the shape of a triangle with a base of 21 ft and a height of 13 ft. Find the area of the vegetable garden.Athletic Fields How much artificial turf should be purchased to cover an athletic field that is in the shape of a trapezoid with a height of 15 m and bases that measure 45 m and 36 m?33ESParks and Recreation A city plans to plant grass seed in a public playground that has the shape of a triangle with a height of 24 m and a base of 20 m. Each bag of grass seed will seed 120 m2. How many bags of seed should be purchased?35ES36ES37ES38ESCarpeting You want to install wall-to-wall carpeting in the family room. The floor plan is shown below. If the cost of the carpet you would like to purchase is $38 per square yard, what is the cost of carpeting your family room? Assume that there is no waste. Hint: 9ft2=1yd2.Interior Decorating You want to paint the rectangular walls of your bedroom. Two walls measure 16 ft by 8 ft. and the other two walls measure 12 ft by 8 ft. The paint you wish to purchase costs $28 per gallon, and each gallon will cover 400 ft2 of wall. Find the minimum amount you will need to spend on paint.41ES42ESCarpentry Find the length of molding needed to put around a circular table that is 4.2 ft in diameter. Round to the nearest hundredth of a foot.Sewing How much binding is needed to bind the edge of a circular rug that is 3 m in diameter? Round to the nearest hundredth of a meter.Pulleys A pulley system is diagrammed below. If pulley B has a diameter of 16 in. and is rotating at 240 revolutions per minute, how far does a given point on the belt travel each minute that the pulley system is in operation? Assume the belt does not slip as the pulley rotates. Round to the nearest inch.Bicycles A bicycle tire has a diameter of 18 in. How many feet does the bicycle travel when the wheel makes 20 revolutions? Round to the nearest hundredth of a foot.47ES48ESIrrigation An irrigation system waters a circular field that has a 50-foot radius. Find the exact area watered by the irrigation system.50ES51ES52ESLake Tahoe One way to measure the area of an irregular figure, such as a lake, is to divide the area into trapezoids that have the same height. Then measure the length of each base, calculate the area of each trapezoid, and add the areas. The following figure gives approximate dimensions for Lake Tahoe, which straddles the California and Nevada borders. Approximate the area of Lake Tahoe using the given trapezoids. Round to the nearest tenth of a square mile.54ES55ES56ES57ESA circle with radius r and circumference C is sliced into 16 identical sectors which are then arranged as shown below. The exterior of this figure resembles a parallelogram, and the figure has the same area as the circle. The exterior of the figure shown by the rearranged sectors resembles a parallelogram. What dimension of the circle approximates the height of the parallelogram? What dimension of the circle approximates the base of the parallelogram? Explain how the formula for the area of a circle can be derived by using this slicing approach.Herons (or Heros) formula is sometimes used to calculate the area of a triangle. Herons Formula The area of a triangle with sides of lengths a, b, and c is given by A=s(sa)(ab)(sc) where s is the semi perimeter of the triangle: s=a+b+c2 Use Herons formula to find the area of a triangle with sides that measure 4.4 in., 5.7 in., and 6.2 in. Round to the nearest tenth of a square inch. Use Herons formula to find the area of an equilateral triangle with sides that measure 8.3 cm. Round to the nearest tenth of a square centimeter. Find the lengths of the sides of a triangle that has a perimeter of 12 in., given that the length of each side, in inches, is a counting number and the area of the triangle, in square inches, is also a counting number. Hint: All three sides are different lengths.Name the genus of each figure. a. Funnel b. Ships wheel c. Axe d. Car steering wheelWhich one of the following figures is not topologically equivalent to the others?Which one of the following figures is not topologically equivalent to the others? Comb Spatula Block OarIn parts a and b, the letters of the alphabet are displayed using a particular font. List all the topogically equivalent letters according to their genus of 0, 1, or 2.5EE6EEFind the ratio of the lengths of corresponding sides for the similar triangles.2ES3ESFind the ratio of the lengths of corresponding sides for the similar triangles.5ESTriangles ABC and DEF are similar triangles. Use this fact to solve each exercise. Round to the nearest tenth. Find side DE.Triangles ABC and DEF are similar triangles. Use this fact to solve each exercise. Round to the nearest tenth. Find the height of triangle DEF.Triangles ABC and DEF are similar triangles. Use this fact to solve each exercise. Round to the nearest tenth. Find the height of triangle ABC.Triangles ABC and DEF are similar triangles. Use this fact to solve each exercise. Round to the nearest tenth. Find the perimeter of triangle ABC.Triangles ABC and DEF are similar triangles. Use this fact to solve each exercise. Round to the nearest tenth. Find the perimeter of triangle DEF.Triangles ABC and DEF are similar triangles. Use this fact to solve each exercise. Round to the nearest tenth. Find the perimeter of triangle ABC.12ES13ES14ESThe given triangles are similar triangles. Use this fact to solve each exercise. Find the height of the flagpole.16ES17ESThe given triangles are similar triangles. Use this fact to solve each exercise. Find the height of the building.The given triangles are similar triangles. Use this fact to solve each exercise. Find the height of the flagpole.20ESIn the figure below, ACDE, BD measures 8 m, AD measures 12 m, and BE measures 6 m. Find the length of BC.22ESIn the figure below, AEBD, AB = 3 ft, ED = 4 ft, and BC = 3 ft. Find the length of CE.24ESIn the figure below, MP and NQ intersect at O, NO = 24 cm, MN = 10 cm, MP = 39 cm, and QO = 12 cm. Find the Length of OP.26ESSurveying Surveyors use similar triangles to measure distances that cannot be measured directly. This is illustrated in Exercises 27 and 28. The diagram below represents a river of width CD. Triangles AOB and DOC are similar. The distances AB, BO, and OC were measured and found to have the lengths given in the diagram. Find CD, the width of the river.Surveying Surveyors use similar triangles to measure distances that cannot be measured directly. This is illustrated in Exercises 27 and 28. The diagram below shows how surveyors laid out similar triangles along the Winnepaugo River. Find the width, d, of the river. Â29ES30ESDetermine whether the two triangles are congruent. If they are congruent, state by what theorem (SSS, SAS, or ASA) they are congruent.32ES33ES34ESDetermine whether the two triangles are congruent. If they are congruent, state by what theorem (SSS, SAS, or ASA) they are congruent.36ESGiven triangle ABC and triangle DEF, do the conditions mC=mE, AC = EF, and BC = DE guarantee that triangle ABC is congruent to triangle DEF? If they are congruent, by what theorem are they congruent?Given triangle PQR and triangle MNO, do the conditions PR = NO, PQ = MO, and QR = MN guarantee that triangle PQR is congruent to triangle MNO? If they are congruent, by what theorem are they congruent?Given triangle LMN and triangle QRS, do the conditions mM=mS, mN=mQ, and, mL=mR guarantee that triangle LMN is congruent to triangle QRS? If they are congruent, by what theorem are they congruent?Given triangle DEF and triangle JKL, do the conditions mD=mK, mE=mL, and DE=KL guarantee that triangle DEF is congruent to triangle JKL If they are congruent, by what theorem are they congruent?41ES42ES43ES44ESFind the length of the unknown side of the triangle. Round to the nearest tenth.46ES47ES48ESFind the length of the unknown side of the triangle. Round to the nearest tenth.50ES51ES52ES53ES54ES55ESUse the given information to solve each exercise. Round to the nearest tenth. Perimeter Find the perimeter of a right triangle with legs that measure 6 in. and 8 in.57ES58ESA cylinder with a 2-cm radius and a height of 10 cm is submerged in a tank of water that is 20 cm wide and 30 cm long (sec Figure 1). How much does the water level rise? Round to the nearest hundredth of a centimeter.A sphere with a radius of 6 in. is placed in a rectangular tank of water that is 16 in. wide and 20 in. long (see Figure 2). The sphere displaces water until two-thirds of the sphere, with respect to its volume, is submerged. How much does the water level rise? Round to the nearest hundredth of an inch.A chemist wants to know the density of a statue that weighs 15 lb. The statue is placed in a rectangular tank of water that is 12 in. long and 12 in. wide (see Figure 3 on page 413). The water level rises 0.42 in. Find the density of the statue. Round to the nearest hundredth of a pound per cubic inch. Hint: Density = weight Ă· volume.1ESFind the volume of the figure. For calculations involving , give both the exact value and an approximation to the nearest hundredth of a unit.Find the volume of the figure. For calculations involving , give both the exact value and an approximation to the nearest hundredth of a unit.4ES5ESFind the volume of the figure. For calculations involving , give both the exact value and an approximation to the nearest hundredth of a unit.7ES8ES9ES10ESFind the surface area of the figure. For calculations involving , give both the exact value and an approximation to the nearest hundredth of a unit.Find the surface area of the figure. For calculations involving , give both the exact value and an approximation to the nearest hundredth of a unit.Solve. Volume A rectangular solid has a length of 6.8 m, a width of 2.5 m, and a height of 2 m. Find the volume of the solid.14ES15ES16ES17ES18ESSolve. Volume The diameter of the base of a cylinder is 24 cm. The height of the cylinder is 18 cm. Find the volume of the cylinder. Round to the nearest hundredth of a cubic centimeter.20ES21ES22ES23ES24ESSolve. The length of a side of a cube is equal to the radius of a sphere. Which solid has the greater volume?Solve. A sphere and a cylinder have the same radius. The height of the cylinder is equal to the radius of its base. Which solid has the greater volume?27ES28ES29ES30ES31ES32ESSolve. Surface Area Find the exact surface area of a sphere with a diameter of 15 cm.34ESSolve. Surface Area The radius of the base of a cylinder is 4 in. The height of the cylinder is 12 in. Find the surface area of the cylinder. Round to the nearest hundredth of a square inch.36ESSolve. Surface Area The slant height of a cone is 2.5 ft. The radius of the base is 1.5 ft. Find the exact surface area of the cone. The formula for the surface area of a cone is given on page 411.38ES39ES40ESSolve. Appliances The volume of a freezer that is a rectangular solid with a length of 7 ft and a height of 3 ft is 52.5 in3. Find the width of the freezer.42ESSolve. Paint A can of paint will cover 300 ft2 of surface. How many cans of paint should be purchased to paint a cylinder that has a height of 30 ft and a radius of 12 ft?Solve. Ballooning A hot air balloon is in the shape of a sphere. Approximately how much fabric was used to construct the balloon if its diameter is 32 ft? Round to the nearest square foot.45ESFind the volume of the figure. Round to the nearest hundredth of a unit.Find the volume of the figure. Round to the nearest hundredth of a unit.Find the volume of the figure. Round to the nearest hundredth of a unit.49ESFind the volume of the figure. Round to the nearest hundredth of a unit.Find the volume of the figure. Round to the nearest hundredth of a unit.Find the surface area of the figure. Round to the nearest hundredth of a unit.Find the surface area of the figure. Round to the nearest hundredth of a unit.54ES55ESOil Tanks A truck is carrying an oil tank. The tank consists of a circular cylinder with a hemisphere on each end, as shown. If the tank is half full, how many cubic feet of oil is the truck carrying? Round to the nearest hundredth of a cubic foot.Swimming Pools How many liters of water are needed to fill the swimming pool shown below?58ES59ES60ES61ESA sphere fits inside a cylinder as shown in the figure below. The height of the cylinder equals the diameter of the sphere. Show that the surface area of the sphere equals the surface area of the side of the cylinder.63ES64ESExplain how you could cut through a cube so that the face of the resulting solid is a square. an equilateral triangle. a trapezoid. a hexagon.Draw a horizontal line segment 10cm long with left endpoint A and right endpoint C. See the diagram at the left.Using a protractor, construct at A a 35° angle.Draw at C a vertical line that intersects the terminal side of angle A at B. Your drawing should be similar to the one at the left.4EE5EE6EE7EE8EE1ES2ESFind the values of sin , cos , and tan for the given right triangle. Give the exact values.Find the values of sin , cos , and tan for the given right triangle. Give the exact values.Find the values of sin , cos , and tan for the given right triangle. Give the exact values.Find the values of sin , cos , and tan for the given right triangle. Give the exact values.Find the values of sin , cos , and tan for the given right triangle. Give the exact values.Find the values of sin , cos , and tan for the given right triangle. Give the exact values.Find the values of sin , cos , and tan for the given right triangle. Give the exact values.Find the values of sin , cos , and tan for the given right triangle. Give the exact values.11ES12ES13ES14ES15ES16ES17ES18ES19ES20ES21ES22ES23ES24ES25ES26ESUse a calculator. Round to the nearest tenth of a degree. Given sin = 0.6239, find .Use a calculator. Round to the nearest tenth of a degree. Given cos = 0.95 16, find .Use a calculator. Round to the nearest tenth of a degree. Find cos1 (0.7536).Use a calculator. Round to the nearest tenth of a degree. Find sin1 (0.4478).31ES32ES33ES34ES35ES36ES37ESUse a calculator. Round to the nearest tenth of a degree. Find tan1 (0.2438).39ES40ES41ES42ESDraw a picture and label it. Then set up an equation and solve it. Show all your work. Round the measure of each angle to the nearest tenth of a degree. Round the length of a side to the nearest tenth of a unit. Assume the ground is level unless indicated otherwise. Ballooning A balloon, tethered by a cable 997 ft long, was blown by a wind so that the cable made an angle of 57.6 with the ground. Find the height of the balloon off the ground.Draw a picture and label it. Then set up an equation and solve it. Show all your work. Round the measure of each angle to the nearest tenth of a degree. Round the length of a side to the nearest tenth of a unit. Assume the ground is level unless indicated otherwise. Roadways A road is inclined at an angle of 9.8° with the horizontal. Find the distance that one must drive on this road in order to be elevated 14.8 ft above the horizontal.Draw a picture and label it. Then set up an equation and solve it. Show all your work. Round the measure of each angle to the nearest tenth of a degree. Round the length of a side to the nearest tenth of a unit. Assume the ground is level unless indicated otherwise. Home Maintenance A ladder 30.8 ft long leans against a building. If the foot of the ladder is 7.25 ft from the base of the building, find the angle the top of the ladder makes with the building.Draw a picture and label it. Then set up an equation and solve it. Show all your work. Round the measure of each angle to the nearest tenth of a degree. Round the length of a side to the nearest tenth of a unit. Assume the ground is level unless indicated otherwise. Aviation A plane takes off from a field and rises at an angle of 11.4° with the horizontal. Find the height of the plane after it has traveled a distance of 1250 ft.Draw a picture and label it. Then set up an equation and solve it. Show all your work. Round the measure of each angle to the nearest tenth of a degree. Round the length of a side to the nearest tenth of a unit. Assume the ground is level unless indicated otherwise. Guy Wires A guy wire whose grounded end is 16 ft from the telephone pole it supports makes an angle of 56.7 with the ground. How long is the wire?Draw a picture and label it. Then set up an equation and solve it. Show all your work. Round the measure of each angle to the nearest tenth of a degree. Round the length of a side to the nearest tenth of a unit. Assume the ground is level unless indicated otherwise. AngIe of Depression A lighthouse built at sea level is 169 ft tall. From its top, the angle of depression to a boat below measures 25.1°. Find the distance from the boat to the foot of the lighthouse.Draw a picture and label it. Then set up an equation and solve it. Show all your work. Round the measure of each angle to the nearest tenth of a degree. Round the length of a side to the nearest tenth of a unit. Assume the ground is level unless indicated otherwise. Angle of Elevation At a point 39.3 ft from the base of a tree, the angle of elevation of its top measures 53.4. Find the height of the tree.50ES51ES52ESDraw a picture and label it. Then set up an equation and solve it. Show all your work. Round the measure of each angle to the nearest tenth of a degree. Round the length of a side to the nearest tenth of a unit. Assume the ground is level unless indicated otherwise. Guy Wires A television transmitter tower is 600 ft high. If the angle between the guy wire (attached at the top) and the tower is 55.4°, how long is the guy wire?Draw a picture and label it. Then set up an equation and solve it. Show all your work. Round the measure of each angle to the nearest tenth of a degree. Round the length of a side to the nearest tenth of a unit. Assume the ground is level unless indicated otherwise. Ramps A ramp used to load a racing car onto a flatbed carrier is 5.25 m long, and its upper end is 1.74 m above the lower end. Find the angle between the ramp and the road.Draw a picture and label it. Then set up an equation and solve it. Show all your work. Round the measure of each angle to the nearest tenth of a degree. Round the length of a side to the nearest tenth of a unit. Assume the ground is level unless indicated otherwise. Angle of Elevation The angle of elevation of the sun is 51.3° at a time when a tree casts a shadow 23.7 yd long. Find the height of the tree.56ES57ES58ES59ES60ESRecall that the circumference of a circle is given by C=2r. Therefore, the radian measure of the central angle subtended by the circumference is =2rr=2. In degree measure, the central angle has a measure of 360. Thus we have 2 radians = 360. Dividing each side of the equation by 2 gives radians = 180. From the last equation, we can establish the conversion factors radians180 and 180radians. These conversion factors are used to convert between radians and degrees. Conversion Between Radians and Degrees To convert from degrees to radians, multiply by radians 180 . To convert from radians to degrees, multiply by 180 radians . For instance, to convert 30 to radians, multiply 30 by radians180. 30=30(radians180)=6radianExactanswer0.5236radianApporximateanswer To convert 2 radians to degrees, multiply 2 by 180radians. 2radians=2(180radians)=(360)Exactanswer114.5916Apporximateanswer What is the measure in degrees of 1 radian?62ES63ES64ES65ES66ES67ES68ES69ES70ES71ES72ES73ES74ES1EE2EE3EE4EE5EE6EE7EE1ES