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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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5 Tests
1. Test2. Test3. Test4. Test5. Test

1. Test

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, what is the hypotenuse?

Please select an answer first.

Correct answer: A

The correct answer is The side opposite the right angle..

  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: The hypotenuse is always opposite the 90-degree angle and is the longest side of a right triangle.
  3. Check the result: The correct answer is The side opposite the right angle..

The hypotenuse is always opposite the 90-degree angle and is the longest side of a right triangle.

2. QuestionMultiple choice

For an acute angle θ, what is sin⁡θ\sin\theta?

Please select an answer first.

Correct answer: B

The correct answer is oppositehypotenuse\frac{\text{opposite}}{\text{hypotenuse}}..

  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 the ratio of the side opposite the angle to the hypotenuse.
  3. Check the result: The correct answer is oppositehypotenuse\frac{\text{opposite}}{\text{hypotenuse}}..

Sine is the ratio of the side opposite the angle to the hypotenuse.

3. QuestionMultiple choice

For an acute angle θ, what is cos⁡θ\cos\theta?

Please select an answer first.

Correct answer: C

The correct answer is adjacenthypotenuse\frac{\text{adjacent}}{\text{hypotenuse}}..

  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 the ratio of the adjacent leg to the hypotenuse.
  3. Check the result: The correct answer is adjacenthypotenuse\frac{\text{adjacent}}{\text{hypotenuse}}..

Cosine is the ratio of the adjacent leg to the hypotenuse.

4. QuestionMultiple choice

For an acute angle θ, what is tan⁡θ\tan\theta?

Please select an answer first.

Correct answer: D

The correct answer is oppositeadjacent\frac{\text{opposite}}{\text{adjacent}}..

  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 the ratio of the opposite leg to the adjacent leg.
  3. Check the result: The correct answer is oppositeadjacent\frac{\text{opposite}}{\text{adjacent}}..

Tangent is the ratio of the opposite leg to the adjacent leg.

5. QuestionMultiple choice

Relative to a chosen acute angle, which side is the opposite side?

Please select an answer first.

Correct answer: A

The correct answer is The side across from the angle..

  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: The opposite side does not touch the reference angle and lies directly across from it.
  3. Check the result: The correct answer is The side across from the angle..

The opposite side does not touch the reference angle and lies directly across from it.

6. QuestionMultiple choice

Relative to a chosen acute angle, which side is the adjacent leg?

Please select an answer first.

Correct answer: B

The correct answer is The leg that touches the angle, not the hypotenuse..

  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: The adjacent leg touches the reference angle and is not the hypotenuse.
  3. Check the result: The correct answer is The leg that touches the angle, not the hypotenuse..

The adjacent leg touches the reference angle and is not the hypotenuse.

7. QuestionMultiple choice

In a 3-4-5 triangle, if the side opposite θ is 3, what is sin⁡θ\sin\theta?

Please select an answer first.

Correct answer: C

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, so sin⁡θ=3/5\sin\theta=3/5.
  3. Check the result: The correct answer is 35\frac{3}{5}..

Sine is opposite over hypotenuse, so sin⁡θ=3/5\sin\theta=3/5.

8. QuestionMultiple choice

In a 5-12-13 triangle, if the leg adjacent to θ is 12, what is cos⁡θ\cos\theta?

Please select an answer first.

Correct answer: D

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: Cosine is adjacent over hypotenuse, so cos⁡θ=12/13\cos\theta=12/13.
  3. Check the result: The correct answer is 1213\frac{12}{13}..

Cosine is adjacent over hypotenuse, so cos⁡θ=12/13\cos\theta=12/13.

9. QuestionMultiple choice

If the opposite side is 8 and the adjacent leg is 15, what is tan⁡θ\tan\theta?

Please select an answer first.

Correct answer: A

The correct answer is 815\frac{8}{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: Tangent is opposite over adjacent, so tan⁡θ=8/15\tan\theta=8/15.
  3. Check the result: The correct answer is 815\frac{8}{15}..

Tangent is opposite over adjacent, so tan⁡θ=8/15\tan\theta=8/15.

10. QuestionMultiple choice

Which identity connects sine and cosine of complementary acute angles?

Please select an answer first.

Correct answer: B

The correct answer is sin⁡θ=cos⁡(90°−θ)\sin\theta=\cos(90°-\theta)..

  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: In a right triangle, the opposite side for one acute angle is the adjacent side for its complement.
  3. Check the result: The correct answer is sin⁡θ=cos⁡(90°−θ)\sin\theta=\cos(90°-\theta)..

In a right triangle, the opposite side for one acute angle is the adjacent side for its complement.

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