To determine the distance between two aircraft, a tracking station continuously determines the distance to each aircraft and the angle between them (see figure). Determine the distance a between the planes when A = 52° miles, b = 22 miles, and c= 19 miles. B.

Q: From a window 30 feet above the level ground, a building 100 feet high, and at a distance of 200…

A:

Q: An aircraft (at Z) is spotted by two observers (at X and Y) who are L = 1750 feet apart. As the…

A: Given: Let XD=x. So, YD=1750-x. In triangle XDZ, ZD=x tan A   and   in triangle ZDY, ZD=(1750-x)…

Q: Please help me find angle C

A: To calculate the angle C in the given right-angled triangle ABC.

Q: A rectangular box has length 14 inches, width 15 inches, and a height of 11 inches. Find the angle…

A:

Q: A tree casts a 25-foot shadow on a sunny day, as shown in the diagram below. 32 - 25 ft – If the…

A: Solution: The objective is to find the height of the tree

Q: A surveyor wishing to find the height of a lighthouse measures the angle A at a point 120 ft. from…

A: Let the height of the light of the lighthouse is h. See the picture below

Q: A state trooper is hidden 35 feet from a highway. One second after a truck passes, the angle …

A: Solution: Let AB =35 feet, θ=15°

Q: A lighthouse is 20 feet tall, and a boat is 50 feet from the base of the lighthouse. What is the…

A:

Q: When a six-foot pole casts a four-foot shadow, what is the angle of elevation of the Sun? Round to…

A: A six-foot pole casts a four-foot shadow. Now the diagrammatic representation is,

Q: A campsite is 8.51 miles from a point directly below the mountain top. If the angle of elevation is…

A:

Q: A building 230 feet tall casts a 40-foot-long shadow. If a person stands at the end of the shadow…

A:

Q: A student stands at point A and measures the angle of elevation to the top of a building at 30°. She…

A:

Q: Find the angle of elevation from point C to point A.

A: Given, ∠A=58°, AB=6m,  ∠B= 90°

Q: Find the angle of elevation from B to C.

A: The angles and sides of a right triangle are related by using trigonometric functions. Trigonometric…

Q: A water main is to be constructed with a 20% grade in the north direction and a 10% grade in the…

A: A water main is to be constructedwith a 20% grade in the north direction and a 10% grade in the east…

Q: Given that csc⁡β>0 and tan⁡β<0 which quadrant does the terminal side of angle β lie?  Explain your…

A:

Q: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts,…

A:

Q: Using the definition of each coordinate direction angle, prove that cos? a + cos? ß + cos? y = 1

A:

Q: Determine value of angle a to the nearest tenth of a degree

A: Given that  sin α=13 in the interval π2&lt;α&lt;π cos β=-13in the interval π&lt;β&lt;3π2

Q: 3. Find the angle of elevation of the sun from the ground to the top of a tree when a tree that is…

A: As per our guidelines we are supposed to do only first question among multiple questions. To get the…

Q: An 18 ft. tree casts a 15 ft. long shadow as shown in the following figure. Which of the following…

A:

Q: Find the measure of the indicated angle to the nearest degree.

A:

Q: Find the value of the angle 0 in degrees rounded to the nearest tenth of a degree. 12

A:

Q: In what quadrant does the terminal side of its positive reference angle lie? A. IV B. III C. I D.…

A:

Q: Find the angle between v and w to the nearest degree.

A: SOLUTION-

Q: Use the law of cosines to find the angle of the triangle based off the sides listed below for…

A:

Q: A building 290 feet tall casts a 100 foot long shadow. If a person stands at the end of the shadow…

A: Given, Building’s height = 290 feet Shadow’s length = 100 feet Person’s height = 5 feet

Q: The angle of elevation is degrees (to the nearest degree)

A:

Q: A rectangular box has length 11 inches, width 20 inches, and a height of 7 inches. Find the angle…

A:

Q: what is the answer to this problem?   Determine the reference angle associated with the given…

A: The given angle is θ=-152°.  The requirement is to find the reference angle of θ=-152° between 0° to…

Q: Two airplanes leave an airport at the same time. An hour later, the planes are 168 km apart. If one…

A: Introduction: The law of cosines for the triangle with sides a, b, c and angles A, B, C is given by,…

Q: A satellite orbiting the earth passes directly overhead at observation stations in Phoenix and Los…

A:

Q: A small aircraft sets a course with a certain bearing and at a speed of 200 mph. A horizontal wind…

A: The angle θ is 3°

Q: A person standing on the street looks up to the top of a building and finds the angle of elevation…

A: Given that the person is standing near the building

Q: A pilot is flying over a straight highway. He determines the angles of depression to two mileposts,…

A: Given: Distance between the milestones is, AB=6.9 km. The two angle of depressions are 35° and 50°.…

Q: From an airplane at an altitude (height) of 1200 m, the angle of depression to a rock on the ground…

A: Given,            From an airplane at an altitude (height) of 1200 m, the angle of depression to a…

Q: From atop a 200-ft lookout tower, a fire is spotted due north through an angle of depression of 12°.…

A: Consider the given figure. Let h be the height of the tower, d be the distance from the fire to the…

Q: An airship is flying at an altitude of 800 m when it spots a village in the distance with a…

A: Consider the diagram given below, Point A is the location of the plane at that instant, point C is…

Q: An 18 ft. tree casts a 15 ft. long shadow as shown in the following figure. Which of the following…

A:

Q: Let 0 be an angle in standard position. In which quadrant or quadrants can 0 be located if it meets…

A: Concept: Below the four quadrants are shown and which trigonometric function is positive in which…

Q: A ship is just off the shore of New York City. A sighting is taken on the Statue of Liberty, which…

A: Given  Height = 305 feet  Base = 950 feet  We need to find the angle of elevation

Q: To find the distance between two small towns, an electronic distance measuring (EDM) instrument is…

A:

Q: A monument is 95 meters highAt an information booth, an observer notices the angle of elevation to…

A:

Q: Find the reference angle and sketch and in standard position. 0 e = 165° a. e' = 5° b. e' = 25° c.…

A: theta=165 degree is in between 90 to 180. So it will be in the second quadrant.

Q: Find the measure of the angle using the reference angle. 3.

A: We know that, a reference angle is the smallest angle that the terminal side of a given angle makes…

Q: Find the angle between u = and v = . If needed, round your answer to the nearest tenth.

A:

Q: Find the measure of the indicated angle to the nearest degree

A:

Q: A ship leaves Port A and travels 59 miles due west to point C. It then adjusts its course 39°…

A: Redraw the figure and consider angle φ which is the angle the ship could have taken wrt west:

Q: Two airplanes leave an airport., and the angle between their flight paths is 40 degrees. An hour…

A: Given query is to find the distance between the airplane after 1 hour.

Q: From her elevated observation post 300 ft away, a naturalist spots a troop of baboons high up in a…

A: Given: From her elevated observation post 300 ft away, a naturalist spots a troop of baboons high up…

Ratios

A ratio is a comparison between two numbers of the same kind. It represents how many times one number contains another. It also represents how small or large one number is compared to the other.

Trigonometric Ratios

Trigonometric ratios give values of trigonometric functions. It always deals with triangles that have one angle measuring 90 degrees. These triangles are right-angled. We take the ratio of sides of these triangles.