Honors Geometry
Trig Word Problems
Name: _______________________________
Angle of Elevation: The angle your line of sight makes with a horizontal line
Angle of Depression: If you look down at an object, the angle your line of sight makes with a horizontal line
1.
You want to hang a banner that is 29 feet tall from the third floor to your school. You need to know
how tall the wall is, but there is a large bush in the way. You throw a 38 foot rope out of the window
to your friend. She extends it to the end and measures the angle of elevation to be 70°. How high is
the window? What if you wanted to find how from the school your friend needs to stand—which trig
ratio should you use?
2.
A ladder rests against a building at a point that is 63 feet above the ground. If the ladder makes a 47°
angle with the ground, what is the length of the ladder?
3.
The Leaning Tower of Pisa is 179 feet high, making a 5.1° angle with the vertical. Find the distance the
base of the building is from the vertical line.
4.
A ski slope has a 42° incline and is 170 yards long. Find the vertical drop.
5.
The Gateway Arch in St. Louis is 630 feet. If a person is walking away from the Arch until the angle of
elevation to the top is 55°, how far from the Arch is the person?
6.
To illuminate the entrance of an apartment building, a night light is mounted on a 6.6 meter pole. If
the base of the poleis 24 meters from the entrance, find the angle of depression of the light.
Honors Geometry
Trig Word Problems
Name: _______________________________
7.
From a sailboat, the angle of elevation to the top of a lighthouse 311 feet away is 17°. Find the
height of the lighthouse.
8.
Write expressions for the tangent of each acute angle in the triangle shown below. Explain how
the tangent of one acute angle is related to the tangent of the other acute angle. What kind of
angle pair are ∠𝐴 and ∠𝐵?
9. You want to build a skateboard ramp with a length of 14 feet and an angle of elevation of 26°. You
to find the height and length of the base of the ramp.
10. A soccer ball is placed 10 ft. away from the goal, which is 8ft. high. You kick the ball and it hits the
crossbar across the top of the goal. What is the angle of elevation of your kick?
11. You are standing on a footbridge in the city park that is 12 ft. high above the pond. You look down
and see a duck in the water 7 ft. away from the footbridge. What is the angle of the depression?
12. Suppose a tree 50 feet in height casts a shadow of length 60 feet. What is the angle of elevation
from the end of the shadow to the top of the tree with respect to the ground?