Solving Right Triangles - Worksheet 3 - 10th Grade

Easy

Find all missing sides and angles of right triangles (Easy)

15 problems · 20-25 minutes · Skills: trigonometry, right triangles, problem solving

About This Worksheet

This easy-level worksheet contains 15 problems designed for 10th Grade students practicing solving right triangles. Easy worksheets use simpler numbers and straightforward problem types to build confidence and reinforce foundational skills.

Solving a right triangle — finding every side and every angle — is a fundamental skill in surveying, navigation, architecture, and physics. The ability to move fluently between sides and angles using trig functions gives students a complete toolkit for working with any right triangle in any applied context.

  • Find all missing side lengths using sine, cosine, and tangent
  • Find all missing angle measures using inverse trig functions
  • Apply the Pythagorean Theorem alongside trig ratios in complete right triangle problems
  • Solve right triangles embedded in geometric figures like hexagons and circles
  • Verify solutions by checking that all angles sum to 180 degrees

How to Solve: Worked Example

Example Problem: A right triangle has an acute angle of 47°. Find the other acute angle.
Solution Steps:
  1. The three angles sum to 180°, and one is exactly 90°.
  2. So the two acute angles sum to 90°.
  3. 90 - 47 = 43°.
Answer: 43°
Tip: The two acute angles of any right triangle are always complementary.
1
A right triangle has an acute angle of 62°. Find the other acute angle.
2
A right triangle has an acute angle of 64°. Find the other acute angle.
3
A right triangle has an acute angle of 55°. Find the other acute angle.
4
A right triangle has an acute angle of 38°. Find the other acute angle.
5
A right triangle has an acute angle of 35°. Find the other acute angle.
6
A right triangle has an acute angle of 56°. Find the other acute angle.
7
A right triangle has an acute angle of 20°. Find the other acute angle.
8
A right triangle has an acute angle of 25°. Find the other acute angle.
9
A right triangle has an acute angle of 54°. Find the other acute angle.
10
A right triangle has an acute angle of 56°. Find the other acute angle.
11
A right triangle has an acute angle of 37°. Find the other acute angle.
12
A right triangle has an acute angle of 58°. Find the other acute angle.
13
A right triangle has an acute angle of 22°. Find the other acute angle.
14
A right triangle has an acute angle of 62°. Find the other acute angle.
15
A right triangle has an acute angle of 44°. Find the other acute angle.

Answer Key

1. 28°2. 26°3. 35°4. 52°5. 55°6. 34°7. 70°8. 65°9. 36°10. 34°11. 53°12. 32°13. 68°14. 28°15. 46°

Frequently Asked Questions

How do I download this solving right triangles - worksheet 3 worksheet?

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How do I find worksheets at different difficulty levels?

Each subtopic has 10 worksheets: Worksheets 1-3 are Easy, 4-7 are Medium, and 8-10 are Hard. Start with Easy worksheets to build confidence, then progress to harder ones.

What skills does this right triangle trigonometry worksheet cover?

This worksheet focuses on trigonometry, right triangles, 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 15 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.