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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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3. 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

A right triangle has hypotenuse 10 and an angle of 30°. What is the opposite side?

Please select an answer first.

Correct answer: A

The correct answer is 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 sin⁡30°=1/2\sin30°=1/2: opposite = 10(1/2)=510(1/2)=5.
  3. Check the result: The correct answer is 5..

Use sin⁡30°=1/2\sin30°=1/2: opposite = 10(1/2)=510(1/2)=5.

2. QuestionMultiple choice

A right triangle has hypotenuse 12 and an angle of 60°. What is the adjacent leg?

Please select an answer first.

Correct answer: B

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 cos⁡60°=1/2\cos60°=1/2: adjacent = 12(1/2)=612(1/2)=6.
  3. Check the result: The correct answer is 6..

Use cos⁡60°=1/2\cos60°=1/2: adjacent = 12(1/2)=612(1/2)=6.

3. QuestionMultiple choice

A right triangle has adjacent leg 8 and angle 45°. What is the opposite side?

Please select an answer first.

Correct answer: C

The correct answer is 8..

  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⁡45°=1\tan45°=1: opposite = 8.
  3. Check the result: The correct answer is 8..

Use tan⁡45°=1\tan45°=1: opposite = 8.

4. QuestionMultiple choice

A right triangle has opposite side 7 and angle 30°. What is the hypotenuse?

Please select an answer first.

Correct answer: D

The correct answer is 14..

  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⁡30°=7/h=1/2\sin30°=7/h=1/2, so h=14.
  3. Check the result: The correct answer is 14..

Use sin⁡30°=7/h=1/2\sin30°=7/h=1/2, so h=14.

5. QuestionMultiple choice

A right triangle has hypotenuse 18 and angle 60°. What is the adjacent leg?

Please select an answer first.

Correct answer: A

The correct answer is 9..

  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⁡60°=9/18=1/2\cos60°=9/18=1/2, so the adjacent leg is 9.
  3. Check the result: The correct answer is 9..

Use cos⁡60°=9/18=1/2\cos60°=9/18=1/2, so the adjacent leg is 9.

6. QuestionMultiple choice

A right triangle has adjacent leg 4 and angle 30°. What is the opposite side?

Please select an answer first.

Correct answer: B

The correct answer is 433\frac{4\sqrt{3}}{3}..

  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⁡30°=1/3\tan30°=1/\sqrt{3}: opposite = 4/3=43/34/\sqrt{3}=4\sqrt{3}/3.
  3. Check the result: The correct answer is 433\frac{4\sqrt{3}}{3}..

Use tan⁡30°=1/3\tan30°=1/\sqrt{3}: opposite = 4/3=43/34/\sqrt{3}=4\sqrt{3}/3.

7. QuestionMultiple choice

What is the hypotenuse of a right triangle with legs 5 and 12?

Please select an answer first.

Correct answer: C

The correct answer is 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 c=52+122=169=13c=\sqrt{5^2+12^2}=\sqrt{169}=13.
  3. Check the result: The correct answer is 13..

Use c=52+122=169=13c=\sqrt{5^2+12^2}=\sqrt{169}=13.

8. QuestionMultiple choice

A 45°-45°-90° triangle has a leg of 7. What is its hypotenuse?

Please select an answer first.

Correct answer: D

The correct answer is 727\sqrt{2}..

  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 45°-45°-90° triangle, the hypotenuse is 2\sqrt{2} times a leg.
  3. Check the result: The correct answer is 727\sqrt{2}..

In a 45°-45°-90° triangle, the hypotenuse is 2\sqrt{2} times a leg.

9. QuestionMultiple choice

A 30°-60°-90° triangle has short leg 6. What is its long leg?

Please select an answer first.

Correct answer: A

The correct answer is 636\sqrt{3}..

  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 side ratio is 1 : 3\sqrt{3} : 2, so the long leg is 636\sqrt{3}.
  3. Check the result: The correct answer is 636\sqrt{3}..

The side ratio is 1 : 3\sqrt{3} : 2, so the long leg is 636\sqrt{3}.

10. QuestionMultiple choice

If tan⁡θ=1\tan\theta=1 for an acute angle, what is θ?

Please select an answer first.

Correct answer: B

The correct answer is 45°..

  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 equals 1 in an isosceles right triangle, whose acute angles are 45 degrees.
  3. Check the result: The correct answer is 45°..

Tangent equals 1 in an isosceles right triangle, whose acute angles are 45 degrees.

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