Angle of Depression and Angle of Elevation
Angle of Depression: The angle measured down from the horizon or a horizontal line.
Angle of Elevation: The angle measured up from the horizon or a horizontal line.
We can find the height of the monument by using the tangent ratio.
Adding 5 ft, the total height of the Washington Monument is 555.54 ft.
A 25 foot tall flagpole casts a 42 foot shadow. What is the angle that the sun hits the flagpole?
Elise is standing on top of a 50 foot building and sees her friend, Molly. If Molly is 30 feet away from the base of the building, what is the angle of depression from Elise to Molly? Elise’s eye height is 4.5 feet.
It might help to draw a picture. Then write and solve a trig equation.
A 20 foot ladder rests against a wall. The base of the ladder is 7 feet from the wall. What angle does the ladder make with the ground?
It might help to draw a picture.
- Kristin is swimming in the ocean and notices a coral reef below her. The angle of depression is
35∘and the depth of the ocean, at that point is 250 feet. How far away is she from the reef?
- The Leaning Tower of Piza currently “leans” at a
4∘angle and has a vertical height of 55.86 meters. How tall was the tower when it was originally built?
Use what you know about right triangles to solve for the missing angle. If needed, draw a picture. Round all answers to the nearest tenth of a degree.
- A 75 foot building casts an 82 foot shadow. What is the angle that the sun hits the building?
- Over 2 miles (horizontal), a road rises 300 feet (vertical). What is the angle of elevation?
- A boat is sailing and spots a shipwreck 650 feet below the water. A diver jumps from the boat and swims 935 feet to reach the wreck. What is the angle of depression from the boat to the shipwreck?
- Standing 100 feet from the base of a building, Sam measures the angle to the top of the building from his eye height to be
50∘. If his eyes are 6 feet above the ground, how tall is the building?
- Over 4 miles (horizontal), a road rises 200 feet (vertical). What is the angle of elevation?
- A 90 foot building casts an 110 foot shadow. What is the angle that the sun hits the building?
- Luke is flying a kite and realizes that 400 feet of string are out. The angle of the string with the ground is
50∘. How high is Luke's kite above the ground?
- An 18 foot ladder rests against a wall. The base of the ladder is 10 feet from the wall. What angle does the ladder make with the ground?
To see the Review answers, open this PDF file and look for section 8.9.