HPC
Right Triangle Trig Applications
Name
Dec. 2014
Angle of Elevation:
Angle of Depression:
How to find 𝜽:
1.
The safety instructions for a 20 ft ladder indicate that the ladder should not be included at more than a 70°
angle with the ground. Suppose the ladder is leaned against a house at this angle, as shown. Find the
following:
a.
The distance from the base of the house to the foot of the ladder
b.
How far up the side of the house the ladder reaches
20 ft
70°
2.
Find the measures of the acute angles of a 3 − 4 − 5 right triangle.
3.
Find the measures of the acute angles of a right triangle whose legs are 9 cm and 16 cm long.
4.
An airplane is at an elevation of 35,000 ft when it begins its approach to an airport. Its angle of descent is 6°.
a.
What is the distance between the airport and the point on the ground directly below the airplane?
b.
What is the approximate air distance between the plane and the airport?
5.
A lighthouse keeper observes that there is a 3° angle of depression between the horizontal and the line of
sight to a ship. If the keeper is 19 m above the water, how far is the ship from shore?
6.
A student looks out of a second-story school window and sees the top of the school flagpole at an angle of
elevation of 22°. The student is 18 ft above the ground and 50 ft from the flagpole. Find the height of the
flagpole.
7.
Find the measures of the angles of an isosceles triangle whose sides are 6, 6, and 8.
8.
Find the measures of the angles of an isosceles triangle whose sides are 5, 10, and 10.
9.
The legs of an isosceles triangle are each 21 cm long and the angle between them has a measure of 52°.
What is the length of the third side?
10.
Points 𝐴 and 𝐵 are on the same side of a tower and are 10 m apart. The angles of elevation of the top of a
tower are 40° and 54° respectively. Find the tower’s height.
11.
A wheelchair ramp must rise 30 inches to meet the front door of a public library. If the ramp’s angle of
elevation is not to exceed 8°, what is the minimum horizontal length of the ramp (in feet)?
12.
A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to
the top of the tree as 71.5°. How tall is the tree? What happens to the angle of elevation if the surveyor
moves further away from the tree?
13.
A skateboard ramp touches the ground at one point, and is 4 ft off the ground at its highest point. The angle
of elevation the ramp makes with the ground is 18.4°. What is the length of the ramp?
14.
A 30-meter line is used to tether a helium filled balloon. Because of a breeze, the line makes an angle of
approximately 75° with the ground. What is the height of the balloon?
15.
In traveling across flat land you notice a mountain directly in front of you. Its angle of elevation to the peak is
3.5°. After you drive 13 miles closer to the mountain, the angle of elevation is 9°. Approximate the height of
the mountain.
16.
A safety regulation states that the maximum angle of elevation for a rescue ladder is 72°. A fire
department’s longest ladder is 110 feet. What is the maximum safe rescue height?
17.
At a point 200 feet from the base of a building, the angle of elevation to the bottom of a smokestack is 35°,
and the angle of elevation to the top of the smokestack is 53°. Find the height of the smokestack.
18.
An engineer builds a 75-foot vertical cellular phone tower. Find the angle of elevation to the top of the
tower from a point on level ground 95 feet from its base.
19.
Find the angle of depression from the top of a lighthouse 250 feet above water to the water line of a ship 2.5
miles offshore.
20.
A ski slope on a mountain has an angle of elevation of 25.2°. The vertical height of the slope is 1808 feet.
How long is the slope?
21.
While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the
peak is 2.5°. After you drive 18 miles closer to the mountain, the angle of elevation is 10°. Approximate the
height of the mountain.
22.
An escalator 152 feet in length rises to a platform and makes 30° angle with the ground. Find the height of
the platform above the ground.
23.
The angle of elevation from the base to the top of a waterslide is 13°. The slide extends horizontally 58.2
meters. Approximate the height of the waterslide.
24.
The sonar of a navy cruiser detects a submarine that is 4000 feet from the cruiser. The angle between the
water level and the submarine is 31.5° How deep is the submarine?
1a. 6.84 ft from the house
1b. 18.8 ft up on the house
2. 36.9°, 53.1°
3. 29.4°, 60.6°
4a. 333,002.8 ft
4b. 334,837.1 ft
5. 362.5 m
6. 38.2 ft
7. 48.2°, 48.2°, 83.6°
8. 75.5°, 75.5°, 29.0°
9. 18.4 cm
10. 21.5 m
11. 17.8 ft
12. 149.43 ft
13. 12.67 ft
14. 28.98 m
15. 1.30 miles
16. 104.62 ft
17. 125.37 ft
18. 38.29°
19. 1.09°
20. 4246.33 ft
21. 1.04 miles
22. 76 ft
23. 13.44 meters
24. 2089.99 ft