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Angles of Elevation & Depression - Worksheet 6 - 10th Grade

Medium

Solve problems with angles of elevation and depression (Medium)

14 problems · 20-25 minutes · Skills: trigonometry, applications, problem solving

About This Worksheet

This medium-level worksheet contains 14 problems designed for 10th Grade students practicing angles of elevation & depression. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Angles of elevation and depression are the most direct application of trigonometry to the real world — used by surveyors to map terrain, architects to calculate roof pitch, pilots to determine glide slope, and astronomers to measure stellar distances. These problems develop the ability to create a mathematical model from a verbal description.

  • Draw and label diagrams for angles of elevation and depression problems
  • Identify the appropriate trig ratio to solve for an unknown height or distance
  • Solve multi-step real-world problems involving angles of elevation and depression
  • Determine heights of buildings or cliffs using two observation points
  • Calculate the angle of a ramp or staircase from horizontal distance and height

How to Solve: Worked Example

Example Problem: A ladder reaches 45 ft up a wall at an angle of elevation of 47°. Find the ladder length.
Solution Steps:
  1. The 45 ft is opposite the angle; the ladder is the hypotenuse.
  2. Use sine: sin 47° = 45/ladder.
  3. ladder = 45 ÷ sin 47° ≈ 45 ÷ 0.7314 ≈ 61.5 ft.
Answer: 61.5
Tip: When the unknown is in the denominator, divide rather than multiply.
1
A ladder reaches 48 ft up a wall at an angle of elevation of 62°. Find the ladder's length (to 1 dp, ft).
2
A ladder reaches 55 ft up a wall at an angle of elevation of 56°. Find the ladder's length (to 1 dp, ft).
3
A ladder reaches 53 ft up a wall at an angle of elevation of 33°. Find the ladder's length (to 1 dp, ft).
4
A ladder reaches 50 ft up a wall at an angle of elevation of 57°. Find the ladder's length (to 1 dp, ft).
5
A ladder reaches 54 ft up a wall at an angle of elevation of 46°. Find the ladder's length (to 1 dp, ft).
6
A ladder reaches 56 ft up a wall at an angle of elevation of 59°. Find the ladder's length (to 1 dp, ft).
7
A ladder reaches 10 ft up a wall at an angle of elevation of 29°. Find the ladder's length (to 1 dp, ft).
8
A ladder reaches 43 ft up a wall at an angle of elevation of 49°. Find the ladder's length (to 1 dp, ft).
9
A ladder reaches 53 ft up a wall at an angle of elevation of 20°. Find the ladder's length (to 1 dp, ft).
10
A ladder reaches 35 ft up a wall at an angle of elevation of 25°. Find the ladder's length (to 1 dp, ft).
11
A ladder reaches 60 ft up a wall at an angle of elevation of 35°. Find the ladder's length (to 1 dp, ft).
12
A ladder reaches 20 ft up a wall at an angle of elevation of 50°. Find the ladder's length (to 1 dp, ft).
13
A ladder reaches 53 ft up a wall at an angle of elevation of 20°. Find the ladder's length (to 1 dp, ft).
14
A ladder reaches 49 ft up a wall at an angle of elevation of 21°. Find the ladder's length (to 1 dp, ft).

Answer Key

1. 54.42. 66.33. 97.34. 59.65. 75.16. 65.37. 20.68. 57.09. 155.010. 82.811. 104.612. 26.113. 155.014. 136.7

Frequently Asked Questions

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What skills does this right triangle trigonometry worksheet cover?

This worksheet focuses on trigonometry, applications, problem solving. It is designed for 10th Grade students and provides structured practice through varied problem types with a worked example to guide students before they begin.

Can I use this worksheet in my classroom?

Yes. All worksheets on K12Worksheets are free for classroom use. You can print copies for your entire class. With 10 worksheets per subtopic at three difficulty levels, you have plenty of options for differentiated instruction and individualized practice.

How many problems are on this worksheet?

This worksheet contains 14 problems. It typically takes 20-25 minutes to complete. An answer key with all solutions is included so parents and teachers can check work quickly.