Alice, Bob, and Catherine stand at different points around the edge of a lake. The distance between Alice and Bob is 158 yards. The distance between Bob and Catherine is 106 yards. Bob estimates that the angle formed from Alice to him to Catherine is 161 degrees. What is the distance between Alice and Catherine to the nearest yard?

Q: Two airplane leave an airport,and the angle between their flight paths is 40°. An hour later, one…

A: Here we have to find the distance between 2 planes by using law of cosines.

Q: the angle of inclination from the base of skyscraper A to the top of the skyscraper B is approx 10.6…

A: We have, the angle of inclination from the base of skyscraper A to the top of the skyscraper B is…

Q: 3) An airplane is sighted at the same time by two ground observers who are 5 miles apart 3 and both…

A: Consider the larger base is x miles to the west of a point down the plane and the observer is 5…

Q: softball the distance from home plate to first base is 60 feet, as is the distance from first base…

A: Let 'd' be distance thrown by catcher standing on home plate to shortstop standing on second base…

Q: A man in a balloon observes two points, A and B, on the horizontal plane. The angle of depression is…

A: The sketch of the given problem is shown below, From triangle DAC,

Q: What angle does the line y = x+ 1 make with the positive side of the line y = 1?

A: Our Aim is to tell angle does the line y=x+1 make with the positive side of the line y=1.

Q: From a helicopter flying at 30,000 feet, the angles of depression of two cities are 28 and 55. How…

A:

Q: fence that is 2.5 m long has started to lean and now makes an angle of 77° with the ground. A 3 m…

A: Given is the length (r) of fence as 2.5 m long. The length of board q  is 3m.  It is required to…

Q: 4. A man whose eye is 1.5 m. above his sole stands on a 48.5 m. high building. The angle of…

A: The height of the man is 1.5 m and he is standing on a building whose height is 48.5 m. So, the…

Q: Relative to the acute angle θ, the three sides of a right triangle are the ________ side, the…

A: Explanation: The longest side of the right triangle, which is also the side opposite the right…

Q: A new homeowner has a triangular-shaped back yard. Two of the three sides measure 65 ft and 80 ft…

A:

Q: A surveyor determines that the angle of elevation to the top of a building from a point on the…

A: To solve the problem, we need to consider that two triangles are formed depending on the distance…

Q: The distance from two golf balls to the hole is 8 feet and 13 feet, respectively. If both balls are…

A: To find: The distance between the golf balls. Given: The distance from two golf balls to the hole is…

Q: A man standing near a radio station antenna observes that the angle of elevation to the top of the…

A:

Q: observation tower is 75 m high. A support wire attached to the tower 20 m from the top. If the…

A: Given query is to find the length of the wire.

Q: In Texas, the distance from Austin to Brownwood is 141 miles. It is 171 miles from Brownwood to…

A: We will use the formula of cosine from SSS triangle to solve this question. Where SSS means "side,…

Q: A person standing on top of a 15-foot high sand pile wishes to estimate the width of the pile. He…

A:

Q: 6. Shakkar, Nic, and Harry are camping in their tents. If the distance between Shakkar and Nic is…

A: As per Bartleby answering guidelines if multiple questions are posted in a single picture and a…

Q: What is the angle of elevation to the kite if a kite is 40 feet off the ground and the string…

A: Consider the diagram drawn as per the given information, here the objective is to find the angle of…

Q: hiking club must determine the width of a stream in order to set up equipment to cross it. If the…

A:

Q: Find the angle between u = (2, - 5) and v = (- 1,4) to the nearest tenth of a degree.

A:

Q: In a triangle, one angle is equal to 60" Find the obtuse angle formed by angle bisectors of the…

A: Considering triangle ABC, Given, Angle A= 60° Let the bisector of angle B and C meet at O.

Q: What is the angle of Angle A in a right triangle whose hypotenuse is 23cm and opposite side is 12cm?

A: Please see the diagram on the white board. It aptly explains the question. ABC is the triangle right…

Q: Find the third angle of a triangle if the sum and difference of the first and second ongle are 100…

A: Given:- The sum and difference of the first and second angle are 100 degrees and 20 degrees,…

Q: wire is attached from the top of a 30-foot tall telephone pole to a stake in the ground. If the…

A: Based on the information given in the problem, you can draw a right triangle like the one shown…

Q: The measure of the angle 330° in standard position is given. Find two positive angles and two…

A:

Q: 5. The angle of elevation of a building 80 m high from a man on the ground is 50.41°. How far is the…

A:

Q: A father wishes to make a home plate for his son to use in practicing baseball. Find the size of…

A: a. We are going to use the following graph. By the assumptions, m∠A=m∠B=m∠C m∠D=m∠E=90°

Q: The distance from two golf balls to the hole is 8 feet and 13 feet, respectively. If both balls are…

A: Graphical representation of the problem: Now, we need to find |BC|.

Q: What would be the angle to a point on a wheel with with coordinates (5,30)?

A: we have to determine the angle to a point on a wheel with coordinate (5,30). as we know that the…

Q: John and Jim are standing on the outside of a circular platform and form a 60 degree angle with the…

A: Since Mike is standing on the platform, he is standing on the circle.

Q: a. Determine the measure of an angle whose measure is 14 times that of its supplement,

A: # As per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: The boat is 3 mi from both light houses and the angle between the line of sight to the lighthouses…

A:

Q: A triangle has one angle of 120°, what must be true about the other two angles?

A: One of the angles of triangle is 180° .    Sum of angles in triangle is 180°    Thus,  Sum of other…

Q: civic group plans to landscape a lot that is located where a road forks and forms an angle of 62°.…

A: A civic group plans to landscape a lot that is located where a road forks and forms an angle of 62°.…

Q: 13. The path from Crossley to Snow House is 600m long. The path from Crossley to Wallace is 40m. If…

A: Given that:                   Distance between Crossley to Snow House, a = 600mDistance between…

Q: An American-Italian high school hockey player from the North Shore is standing 10 feet from a…

A:

Q: The angle of elevation from the top of a 95 foot tall bulding to a hot alr balloon In the sky is 76.…

A:

Q: Tom, Dick, and Harry are camping in their tents. If the distance between Tom and Dick is 153 feet,…

A: Let us denote Tom as A, Dick as B, and Harry as C. As per the question, c=AB=153 feet, b=AC=201…

Q: An airplane is one mile above sea level when it begins to rise at a constant angle of 2 ° for the…

A:

Q: The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A…

A:

Q: The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A…

A:

Q: The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A…

A: Given that: Distance between the two stations =56 mi

Q: Mang Tomas will enclose two sides of his triangular vegetable garden with two pieces of chicken wire…

A:

Q: he height of a right circular cone is 24.6 centimeters. If the diameter of the base is 10.4…

A: Given: The height of a right circular cone is 24.6 cm. The diameter of the base of the cone is 10.4…

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: The angle of elevation from a fishing boat to the top of a lighthouse is 5°. If the top of the…

A:

Q: 1. Stephanie knows that when she stands 123 feet from the base of the flagpole the angle of…

A:

Q: The length of a string from the center of a yo-yo to tip of Tony’s middle finger is 12 cm. If Tony…

A:

Q: The measure of an angle in standard position is given. Find two positive angles and two negative…

A:

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.