Right Triangle Review

Use the Pythagorean Theorem to find the missing side.

1. / 2. Find the perimeter / 3. / 4.

Use the appropriate trig function to solve for the indicated variable. Round your answer to the nearest tenth.

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Use your theorems for 30°-60°-90° and 45°-45°-90° triangles to find the missing sides of each triangle. Leave all answers in simplified radical form.

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Draw and label a sketch for each problem below. Write an equation to find the indicated measure and show all of your work.

  1. A monument stands on level ground. The angle of elevation to the top of the monument, taken at a point 425 feet from the foot of the monument, is 32°. Find the height of the monument to the nearest foot.
  1. A boy flying a kite lets out 150 feet of string that makes an angle of 64 degrees with the ground. Assuming that the string is straight, find to the nearest foot how high the kite is above the ground.
  1. A 25-foot guy wire attached to the top of a pole makes an angle 62° with the ground. Find to the nearest foot the distance between the point where the guy wire meets the ground and the foot of the pole.
  1. Miriam spots two ships. If one ship is 49 miles due west and the second is 68 miles due north of where she stands, how far apart are the ships?
  1. A boy walked 400 feet into a tunnel which slopes downward at an angle of 7 degrees with the horizontal ground. Find to the nearest ten feet how far he was beneath the surface.
  1. Find the length of a radius of a circle whose endpoints are and .
  1. Find the area of an equilateral triangle with sides measuring 14 inches.
  1. An airplane A is 1000 feet above the ground and directly over a church C. The angle of elevation of the plane as seen by a boy at a point B on the ground some distance from the church is 22 degrees. Find to the nearest foot:
  2. How far the boy is from the church
  3. How far the boy is from the plane.
  1. An observer in a balloon which is 2000 feet above an airport finds that the angle of depression of a steamer out at sea is 21 degrees. Find to the nearest hundred feet the distance between the balloon and the steamer.
  1. Max is flying a kite with a 42-foot roll of string that he has completely let out. His friend is standing directly under the kite 15 feet away from Max. How high is the kite? Assume the distance from the ground to Max’s hand holding the string is 3 feet.)
  1. A plane takes off from a field and climbs at an angle of 12 degrees. Find to the nearest 100 feet how far the plane must fly to be at an altitude of 1200 feet.
  1. Find to the nearest degree the angle of elevation of the sun when a tree 24 feet high casts a shadow of 36 feet.
  1. Michelle needs to get to a campsite on the other side of a lake, but the boat is gone from the dock when she arrives. Instead Michelle must walk 10 miles due south, then 24 miles due east to arrive at the camp. How far would she have had to row across the lake to get to camp if the boat had been at the dock?