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Trigonometry Introduction Practice Tests

These Grade 10 Geometry practice tests introduce right-triangle trigonometry through sine, cosine, tangent, special angles, missing sides, and practical measurement problems.

Skills covered

  • Identifying the hypotenuse, opposite side, and adjacent leg relative to an acute angle
  • Using SOHCAHTOA to calculate sine, cosine, and tangent ratios
  • Finding missing sides with trigonometric ratios and the Pythagorean Theorem
  • Using 30°, 45°, and 60° special-angle values and complementary-angle relationships
  • Applying trigonometry to ladders, ramps, shadows, buildings, towers, roofs, cables, and elevation problems

How to use these practice tests

Start by labeling the reference angle and the three sides of the right triangle. Choose sine, cosine, or tangent based on the sides involved, then check whether the answer has a reasonable length and unit.

For more Grade 10 Math practice, return to the Grade 10 Math category.

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Grade 10 Trigonometry Introduction Practice Tests

Practice Grade 10 Geometry questions about right triangles, sine, cosine, tangent, SOHCAHTOA, special angles, inverse reasoning, and real-world applications.

Choose the best answer. Identify the reference angle and the opposite, adjacent, and hypotenuse sides before selecting a ratio or special-angle relationship.

10 Questions
0/10 Questions0 %
Correct 0
Incorrect 0
Unanswered 10
1. QuestionMultiple choice

In a right triangle, the opposite side is 6 and the hypotenuse is 10. What is sin⁡θ\sin\theta?

Please select an answer first.

Correct answer: A

The correct answer is 35\frac{3}{5}..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: Use sine: sin⁡θ=6/10=3/5\sin\theta=6/10=3/5.
  3. Check the result: The correct answer is 35\frac{3}{5}..

Use sine: sin⁡θ=6/10=3/5\sin\theta=6/10=3/5.

2. QuestionMultiple choice

In a right triangle, the adjacent leg is 12 and the hypotenuse is 13. What is cos⁡θ\cos\theta?

Please select an answer first.

Correct answer: B

The correct answer is 1213\frac{12}{13}..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: Use cosine: cos⁡θ=12/13\cos\theta=12/13.
  3. Check the result: The correct answer is 1213\frac{12}{13}..

Use cosine: cos⁡θ=12/13\cos\theta=12/13.

3. QuestionMultiple choice

In a right triangle, the opposite side is 7 and the adjacent leg is 24. What is tan⁡θ\tan\theta?

Please select an answer first.

Correct answer: C

The correct answer is 724\frac{7}{24}..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: Use tangent: tan⁡θ=7/24\tan\theta=7/24.
  3. Check the result: The correct answer is 724\frac{7}{24}..

Use tangent: tan⁡θ=7/24\tan\theta=7/24.

4. QuestionMultiple choice

A right triangle has opposite side 9, adjacent leg 12, and hypotenuse 15. What is sin⁡θ\sin\theta?

Please select an answer first.

Correct answer: D

The correct answer is 35\frac{3}{5}..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: Sine is opposite over hypotenuse: 9/15=3/59/15=3/5.
  3. Check the result: The correct answer is 35\frac{3}{5}..

Sine is opposite over hypotenuse: 9/15=3/59/15=3/5.

5. QuestionMultiple choice

If the adjacent leg is 8 and the hypotenuse is 17, what is cos⁡θ\cos\theta?

Please select an answer first.

Correct answer: A

The correct answer is 817\frac{8}{17}..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: Cosine is adjacent over hypotenuse, so the ratio is 8/178/17.
  3. Check the result: The correct answer is 817\frac{8}{17}..

Cosine is adjacent over hypotenuse, so the ratio is 8/178/17.

6. QuestionMultiple choice

If the opposite side is 5 and the adjacent leg is 12, what is tan⁡θ\tan\theta?

Please select an answer first.

Correct answer: B

The correct answer is 512\frac{5}{12}..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: Tangent is opposite over adjacent, so tan⁡θ=5/12\tan\theta=5/12.
  3. Check the result: The correct answer is 512\frac{5}{12}..

Tangent is opposite over adjacent, so tan⁡θ=5/12\tan\theta=5/12.

7. QuestionMultiple choice

If sin⁡θ=12\sin\theta=\frac{1}{2} and the hypotenuse is 14, what is the opposite side?

Please select an answer first.

Correct answer: C

The correct answer is 7..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: Use sin⁡θ=opposite/14=1/2\sin\theta=\text{opposite}/14=1/2, giving opposite = 7.
  3. Check the result: The correct answer is 7..

Use sin⁡θ=opposite/14=1/2\sin\theta=\text{opposite}/14=1/2, giving opposite = 7.

8. QuestionMultiple choice

If cos⁡θ=45\cos\theta=\frac{4}{5} and the hypotenuse is 20, what is the adjacent leg?

Please select an answer first.

Correct answer: D

The correct answer is 16..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: Use cos⁡θ=adjacent/20=4/5\cos\theta=\text{adjacent}/20=4/5, so adjacent = 16.
  3. Check the result: The correct answer is 16..

Use cos⁡θ=adjacent/20=4/5\cos\theta=\text{adjacent}/20=4/5, so adjacent = 16.

9. QuestionMultiple choice

If tan⁡θ=34\tan\theta=\frac{3}{4} and the adjacent leg is 8, what is the opposite side?

Please select an answer first.

Correct answer: A

The correct answer is 6..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: Use tan⁡θ=opposite/8=3/4\tan\theta=\text{opposite}/8=3/4, so opposite = 6.
  3. Check the result: The correct answer is 6..

Use tan⁡θ=opposite/8=3/4\tan\theta=\text{opposite}/8=3/4, so opposite = 6.

10. QuestionMultiple choice

What is the hypotenuse of a right triangle with legs 9 and 12?

Please select an answer first.

Correct answer: B

The correct answer is 15..

  1. Identify the right-triangle information: Label the angle, opposite side, adjacent leg, and hypotenuse before choosing a trigonometric ratio.
  2. Apply the trigonometric relationship: By the Pythagorean Theorem, c=92+122=225=15c=\sqrt{9^2+12^2}=\sqrt{225}=15.
  3. Check the result: The correct answer is 15..

By the Pythagorean Theorem, c=92+122=225=15c=\sqrt{9^2+12^2}=\sqrt{225}=15.

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