Start free
Back to the topic
Free printable worksheetlessoons.com

Trigonometry in the Right Triangle · Ages 15–16

Angles of Elevation and Depression Practice

Name: Date:

Designed for 10th-grade trigonometry students. Solve each problem by identifying the reference angle and choosing the correct trigonometric ratio. Round side lengths to the nearest tenth.

  1. True or False: An angle of depression is measured between a vertical wall and your line of sight.

  2. A climber on a cliff looks down at a hiker at an angle of depression of 34 degrees. What is the angle of elevation from the hiker to the climber?

  3. You stand 20 meters from the base of a monument. Looking at the top, your angle of elevation is 40 degrees. Your eye level is not considered. Find the height of the monument using tan(40°) ≈ 0.839.

  4. Repeat item 3, but now assume your eye height is 1.6 meters above the ground. What is the total height of the monument?

  5. From the top of a 30-meter lighthouse, a keeper spots a boat at an angle of depression of 25 degrees. Find the horizontal distance from the lighthouse base to the boat using tan(25°) ≈ 0.466.

  6. A 12-meter ladder leans against a wall, making an angle of elevation with the ground of 65 degrees. How high up the wall does the ladder reach? Use sin(65°) ≈ 0.906.

More topics and worksheets at lessoons.com© 2026 Lessons · 1 / 2
Answer keylessoons.com

Angles of Elevation and Depression Practice

Answer key

  1. True or False: An angle of depression is measured between a vertical wall and your line of sight.

    False. Both angles of elevation and depression must be measured from a horizontal line of sight.

  2. A climber on a cliff looks down at a hiker at an angle of depression of 34 degrees. What is the angle of elevation from the hiker to the climber?

    34 degrees. The angle of depression and angle of elevation between two points are equal alternate interior angles.

  3. You stand 20 meters from the base of a monument. Looking at the top, your angle of elevation is 40 degrees. Your eye level is not considered. Find the height of the monument using tan(40°) ≈ 0.839.

    16.8 meters. Setup: tan(40°) = height / 20. Height = 20 × 0.839 = 16.78 meters, which rounds to 16.8 meters.

  4. Repeat item 3, but now assume your eye height is 1.6 meters above the ground. What is the total height of the monument?

    18.4 meters. Add eye height to the triangle height: 16.8 + 1.6 = 18.4 meters.

  5. From the top of a 30-meter lighthouse, a keeper spots a boat at an angle of depression of 25 degrees. Find the horizontal distance from the lighthouse base to the boat using tan(25°) ≈ 0.466.

    64.4 meters. Setup: tan(25°) = 30 / distance. Distance = 30 / 0.466 ≈ 64.38 meters, which rounds to 64.4 meters.

  6. A 12-meter ladder leans against a wall, making an angle of elevation with the ground of 65 degrees. How high up the wall does the ladder reach? Use sin(65°) ≈ 0.906.

    10.9 meters. Setup: sin(65°) = height / 12. Height = 12 × 0.906 = 10.87 meters, which rounds to 10.9 meters.