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Trigonometry Applications
1. From a point 30 ft away from the foot of a tower, the angle of elevation of the top of the tower is
60°. What is the height of the tower?
2. A steel wire is tied from a point on the ground to the top of an electric pole whose height is 20 ft.
The wire makes an angle of 70° with the horizontal through the foot of the pole. Find the length of the
wire.
3. If the base of an isosceles triangle is 40 cm long and the vertex angle measures 50°, then what is
the length of each leg?
4. A building is 60 ft tall. From the top of the building, the angles of depression of two cars standing
(one directly behind the other) on the road are 35° and 65°. What is the distance between the cars?
5. A man on the deck of a ship is 23 ft above water level. He observes that the angle of elevation of
the top of a cliff is 50° and the angle of depression of the base is 30°. Find the distance of the cliff
from the ship and the height of the cliff if the base of the cliff is at sea level.
6. Find the measure of angle θ in the figure.
7. A man is standing on the deck of a ship, which is 10 ft above water level. He observes the angle of
elevation of the top of a hill as 75° and the angle of depression of the base of the hill as 45°. Find the
height of the hill if its base is at sea level.
8. A flagstaff stands upon the top of a building. From a distance of 200 ft, the angles of elevation of
the tops of the building and flagstaff are 37° and 48°. What is the length of the flagstaff ?