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Angles of Elevation & Depression - Worksheet 3 - 10th Grade

Easy

Solve problems with angles of elevation and depression (Easy)

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

About This Worksheet

This easy-level worksheet contains 12 problems designed for 10th Grade students practicing angles of elevation & depression. Easy worksheets use simpler numbers and straightforward problem types to build confidence and reinforce foundational skills.

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 40 ft away, the angle of elevation to a treetop is 20°. Find the height.
Solution Steps:
  1. The height is opposite the angle; the 40 ft is adjacent.
  2. Use tangent: tan 20° = height/40.
  3. height = 40 × tan 20° ≈ 40 × 0.3640 ≈ 14.6 ft.
Answer: 14.6
Tip: Sketch the triangle and label which side is opposite and which is adjacent before choosing a ratio.
1
From 53 ft away, the angle of elevation to the top of a tree is 46°. Find the tree's height (to 1 dp, ft).
2
From 60 ft away, the angle of elevation to the top of a tree is 32°. Find the tree's height (to 1 dp, ft).
3
From 67 ft away, the angle of elevation to the top of a tree is 50°. Find the tree's height (to 1 dp, ft).
4
From 16 ft away, the angle of elevation to the top of a tree is 56°. Find the tree's height (to 1 dp, ft).
5
From 70 ft away, the angle of elevation to the top of a tree is 29°. Find the tree's height (to 1 dp, ft).
6
From 57 ft away, the angle of elevation to the top of a tree is 54°. Find the tree's height (to 1 dp, ft).
7
From 51 ft away, the angle of elevation to the top of a tree is 61°. Find the tree's height (to 1 dp, ft).
8
From 49 ft away, the angle of elevation to the top of a tree is 48°. Find the tree's height (to 1 dp, ft).
9
From 26 ft away, the angle of elevation to the top of a tree is 62°. Find the tree's height (to 1 dp, ft).
10
From 40 ft away, the angle of elevation to the top of a tree is 30°. Find the tree's height (to 1 dp, ft).
11
From 19 ft away, the angle of elevation to the top of a tree is 21°. Find the tree's height (to 1 dp, ft).
12
From 37 ft away, the angle of elevation to the top of a tree is 30°. Find the tree's height (to 1 dp, ft).

Answer Key

1. 54.92. 37.53. 79.84. 23.75. 38.86. 78.57. 92.08. 54.49. 48.910. 23.111. 7.312. 21.4

Frequently Asked Questions

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Click the "Download PDF / Print" button at the top of the worksheet. You can save it as a PDF or print it directly. The answer key will be on a separate page.

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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 12 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.