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

Hard

Solve problems with angles of elevation and depression (Hard)

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

About This Worksheet

This hard-level worksheet contains 18 problems designed for 10th Grade students practicing angles of elevation & depression. Hard worksheets feature challenging problems including multi-step questions, missing values, and real-world applications to push students further.

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: From a cliff 182 ft high, the angle of depression to a boat is 62°. Find the distance to the cliff base.
Solution Steps:
  1. The angle of depression from the cliff equals the angle of elevation from the boat.
  2. The cliff height is opposite; the ground distance is adjacent.
  3. tan 62° = 182/distance, so distance = 182 ÷ tan 62°.
  4. ≈ 182 ÷ 1.8807 ≈ 96.8 ft.
Answer: 96.8
Tip: Depression and elevation angles are equal alternate interior angles — measure from the horizontal, never the vertical.
1
From a cliff 177 ft high, the angle of depression to a boat is 29°. Find the boat's distance from the cliff base (to 1 dp, ft).
2
From a cliff 216 ft high, the angle of depression to a boat is 37°. Find the boat's distance from the cliff base (to 1 dp, ft).
3
From a cliff 60 ft high, the angle of depression to a boat is 34°. Find the boat's distance from the cliff base (to 1 dp, ft).
4
From a cliff 146 ft high, the angle of depression to a boat is 22°. Find the boat's distance from the cliff base (to 1 dp, ft).
5
From a cliff 201 ft high, the angle of depression to a boat is 64°. Find the boat's distance from the cliff base (to 1 dp, ft).
6
From a cliff 83 ft high, the angle of depression to a boat is 30°. Find the boat's distance from the cliff base (to 1 dp, ft).
7
From a cliff 98 ft high, the angle of depression to a boat is 54°. Find the boat's distance from the cliff base (to 1 dp, ft).
8
From a cliff 149 ft high, the angle of depression to a boat is 29°. Find the boat's distance from the cliff base (to 1 dp, ft).
9
From a cliff 126 ft high, the angle of depression to a boat is 30°. Find the boat's distance from the cliff base (to 1 dp, ft).
10
From a cliff 300 ft high, the angle of depression to a boat is 36°. Find the boat's distance from the cliff base (to 1 dp, ft).
11
From a cliff 269 ft high, the angle of depression to a boat is 42°. Find the boat's distance from the cliff base (to 1 dp, ft).
12
From a cliff 233 ft high, the angle of depression to a boat is 61°. Find the boat's distance from the cliff base (to 1 dp, ft).
13
From a cliff 97 ft high, the angle of depression to a boat is 25°. Find the boat's distance from the cliff base (to 1 dp, ft).
14
From a cliff 138 ft high, the angle of depression to a boat is 54°. Find the boat's distance from the cliff base (to 1 dp, ft).
15
From a cliff 52 ft high, the angle of depression to a boat is 34°. Find the boat's distance from the cliff base (to 1 dp, ft).
16
From a cliff 233 ft high, the angle of depression to a boat is 23°. Find the boat's distance from the cliff base (to 1 dp, ft).
17
From a cliff 262 ft high, the angle of depression to a boat is 37°. Find the boat's distance from the cliff base (to 1 dp, ft).
18
From a cliff 84 ft high, the angle of depression to a boat is 53°. Find the boat's distance from the cliff base (to 1 dp, ft).

Answer Key

1. 319.32. 286.63. 89.04. 361.45. 98.06. 143.87. 71.28. 268.89. 218.210. 412.911. 298.812. 129.213. 208.014. 100.315. 77.116. 548.917. 347.718. 63.3

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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.

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How many problems are on this worksheet?

This worksheet contains 18 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.