Name:
Ms. D’Amato & Ms. Reeves
Date:
Block:
Trigonometric Applications
An angle of elevation is the angle formed as you look up at an object above you. One side of the angle is your
line of sight; the other side of the angle is the ground or a line parallel to the ground.
Angle of
elevation
An angle of depression is the angle formed as you look down at an object below you. One side of the angle is
the line of sight; the other side is a line parallel to the ground.
Angle of depression
These angles can be used with trig to find the heights of objects that would be difficult to measure otherwise.
Example 1:
You are looking at a tree that you know is 25 feet high, the angle of elevation to the top of the tree is 28. Find
how far away you are from the tree.
Example 2:
A person standing at the top of a 125-foot tall building sights a friend on the ground. The angle of depression is
52. How far is the friend from the base of the building?
Draw diagrams to solve each problem. Round answers to the nearest tenth.
1.] From a spot 40 feet from the base of a tree, the angle of elevation to the top of the tree is 28. Find the
height of the tree.
2.] A person standing at the top of a 100-foot tall building sights a friend on the ground. The angle of
depression is 52. How far is the friend from the base of the building?
3.] The angle of elevation from the base to the top of a waterslide is 13. The length of the slide is 150 feet.
Find the height of the slide.
4.] The angle of depression from the top of a ski slope to the bottom is 20. The elevation at the top of the
slope is 5500 feet and the elevation at the bottom of the slope is 5018 feet. Find the length of the ski slope.
5.] Standing 120 feet from the base of a building, you determine that the angle of elevation to the top of the
building is 48. Find the height of the building.
6.] The ground crew for a hot air balloon sees the balloon in the sky at an angle of elevation of 11. The pilot
radios to the crew that the balloon is 950 feet above the ground. What is the horizontal distance between the
balloon and the ground crew?
7.] From the top of a lighthouse, a Coast Guard worker spots a ship in distress, at an angle of depression of 22.
If he knows that the lighthouse is 120 feet tall, how far from shore should he tell the rescue ship to search?
8.] Alvin is standing at the top of a 50-foot building and sees his friends Bob and Carol on the street below. If
the angle of depression to where Bob is standing is 24º and the angle of depression to where Carol is standing is
17º, how far apart are Bob and Carol?