Download Name Geometry Date ______ Soh Cah Toa Story Problems For

Name _______________________________
Geometry
Date _____________________Hour ______
Soh Cah Toa Story Problems
For each problem you must draw a diagram, set up the trig problem then solve. Round all lengths to the
nearest tenth, and all angles to the nearest degree.
1) A 10-meter ladder is leaning against the side of a building. If the foot of the ladder is 3 meters from
the base of the building find the measure of the acute angle that the ladder makes with the building.
2) A kite string is 200 meters long. Find the height of the kite if the string makes an angle of 38° with the
ground. (Assume the kite string does not sag.)
3) An isosceles triangle has equal legs of 15 cm and the altitude to the base of the triangle is 12 cm. Find
the measure of the base angles.
4) A telegraph pole is stayed by wires to the ground from a point 20 feet up the pole. Each of the wires
makes an angle of 24° with the vertical pole. Find the length of the wire.
5) From a point on the ground, at the end of the shadow, to the top of a tree, the angle of elevation
is 34°. The shadow of the tree is 44 feet long. Find the height of the tree.
6) In a right triangle ABC, BC = 174.92 ft., and AB = 200 ft. If angle C is the right angle, find the measure of
angle B.
7) The guy wire is attached to the top of a 75 meter tower. The wire meets the ground at a 65° angle.
Find the length of the wire.
8) From the top of Goat Island Lighthouse, the angle of depression to a ship at sea is 2°. If the lighthouse
is 60 feet above sea level, find the distance from the base of the lighthouse to the ship.
9) The pilot of an airplane must begin his descent, he is at an altitude of 6000 meters and is 68,500
meters from his point of arrival (land distance) what will be his angle of depression?
10) A hill that is used for sledding has an angle of elevation of 30°. If the length of the sledder’s ride is 52.6
feet, estimate the height of the hill.
11) The angle of elevation from your position on the ground to the top of a building is 67° and you are
standing 30 meters from the foot of the building. Approximate the height of the building.
12) An airplane is flying at an altitude of 2 miles above the ground. The distance along the ground from
the airplane to the airport is 21 miles. He must begin his angle of descent. What angle is the angle of
decent for the plane?