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Trigonometric Ratios - Worksheet 4 - 10th Grade

Medium

Define and apply sine, cosine, and tangent in right triangles (Medium)

24 problems · 20-25 minutes · Skills: trigonometry, right triangles, ratios

About This Worksheet

This medium-level worksheet contains 24 problems designed for 10th Grade students practicing trigonometric ratios. Medium worksheets introduce larger numbers and varied question formats to deepen understanding and build fluency.

Trigonometric ratios are one of the most powerful tools in all of mathematics, connecting angles to lengths in a way that enables calculation of distances, heights, and positions that cannot be measured directly. They are the gateway to a vast portion of mathematics — from the unit circle to Fourier analysis — and have applications in every field of science and engineering.

  • Define sine, cosine, and tangent as ratios of sides in a right triangle using SOH-CAH-TOA
  • Write the six trigonometric ratios for an acute angle given a right triangle
  • Use a calculator to evaluate trig ratios and inverse trig functions for any acute angle
  • Use reciprocal ratios (cosecant, secant, cotangent) to solve for missing sides
  • Identify co-function relationships between complementary angles

How to Solve: Worked Example

Example Problem: A right triangle has legs 9 (opposite ∠A) and 12 (adjacent), hypotenuse 15. Find tan A.
Solution Steps:
  1. TOA: tangent = opposite ÷ adjacent.
  2. Opposite = 9, adjacent = 12.
  3. tan A = 9/12, which reduces to 3/4.
Answer: 3/4
Tip: Tangent is the only one of the three that ignores the hypotenuse.
1
A right triangle has legs 40 (opposite ∠A) and 9 (adjacent), hypotenuse 41. Find tan A.
2
A right triangle has legs 60 (opposite ∠A) and 11 (adjacent), hypotenuse 61. Find cos A.
3
A right triangle has legs 36 (opposite ∠A) and 15 (adjacent), hypotenuse 39. Find tan A.
4
A right triangle has legs 12 (opposite ∠A) and 5 (adjacent), hypotenuse 13. Find tan A.
5
A right triangle has legs 18 (opposite ∠A) and 24 (adjacent), hypotenuse 30. Find cos A.
6
A right triangle has legs 12 (opposite ∠A) and 35 (adjacent), hypotenuse 37. Find tan A.
7
A right triangle has legs 10 (opposite ∠A) and 24 (adjacent), hypotenuse 26. Find cos A.
8
A right triangle has legs 9 (opposite ∠A) and 12 (adjacent), hypotenuse 15. Find cos A.
9
A right triangle has legs 14 (opposite ∠A) and 48 (adjacent), hypotenuse 50. Find tan A.
10
A right triangle has legs 48 (opposite ∠A) and 14 (adjacent), hypotenuse 50. Find tan A.
11
A right triangle has legs 24 (opposite ∠A) and 18 (adjacent), hypotenuse 30. Find tan A.
12
A right triangle has legs 4 (opposite ∠A) and 3 (adjacent), hypotenuse 5. Find cos A.
13
A right triangle has legs 21 (opposite ∠A) and 20 (adjacent), hypotenuse 29. Find cos A.
14
A right triangle has legs 30 (opposite ∠A) and 16 (adjacent), hypotenuse 34. Find tan A.
15
A right triangle has legs 18 (opposite ∠A) and 24 (adjacent), hypotenuse 30. Find tan A.
16
A right triangle has legs 5 (opposite ∠A) and 12 (adjacent), hypotenuse 13. Find tan A.
17
A right triangle has legs 16 (opposite ∠A) and 63 (adjacent), hypotenuse 65. Find cos A.
18
A right triangle has legs 48 (opposite ∠A) and 55 (adjacent), hypotenuse 73. Find cos A.
19
A right triangle has legs 55 (opposite ∠A) and 48 (adjacent), hypotenuse 73. Find tan A.
20
A right triangle has legs 7 (opposite ∠A) and 24 (adjacent), hypotenuse 25. Find cos A.
21
A right triangle has legs 12 (opposite ∠A) and 16 (adjacent), hypotenuse 20. Find cos A.
22
A right triangle has legs 48 (opposite ∠A) and 55 (adjacent), hypotenuse 73. Find cos A.
23
A right triangle has legs 48 (opposite ∠A) and 14 (adjacent), hypotenuse 50. Find tan A.
24
A right triangle has legs 5 (opposite ∠A) and 12 (adjacent), hypotenuse 13. Find tan A.

Answer Key

1. 40/92. 11/613. 12/54. 12/55. 4/56. 12/357. 12/138. 4/59. 7/2410. 24/711. 4/312. 3/513. 20/2914. 15/815. 3/416. 5/1217. 63/6518. 55/7319. 55/4820. 24/2521. 4/522. 55/7323. 24/724. 5/12

Frequently Asked Questions

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What skills does this right triangle trigonometry worksheet cover?

This worksheet focuses on trigonometry, right triangles, ratios. 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 24 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.