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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. 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 10-foot ladder makes a 30° angle with the ground. How high does it reach on a vertical wall?

Please select an answer first.

Correct answer: A

The correct answer is 5 feet..

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

The height is opposite the angle: 10sin⁡30°=10(1/2)=510\sin30°=10(1/2)=5 feet.

2. QuestionMultiple choice

A ramp rises 3 feet over a horizontal run of 12 feet. What is its slope?

Please select an answer first.

Correct answer: B

The correct answer is 14\frac{1}{4}..

  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: Slope is rise over run: 3/12=1/43/12=1/4.
  3. Check the result: The correct answer is 14\frac{1}{4}..

Slope is rise over run: 3/12=1/43/12=1/4.

3. QuestionMultiple choice

A person stands 20 meters from a building and sees the top at a 45° angle of elevation. How tall is the building, ignoring eye height?

Please select an answer first.

Correct answer: C

The correct answer is 20 meters..

  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: At 45 degrees, tangent is 1, so height = 20tan⁡45°=2020\tan45°=20 meters.
  3. Check the result: The correct answer is 20 meters..

At 45 degrees, tangent is 1, so height = 20tan⁡45°=2020\tan45°=20 meters.

4. QuestionMultiple choice

A 13-foot support cable reaches from the ground to a point on a wall 5 feet from the wall. How high is the point?

Please select an answer first.

Correct answer: D

The correct answer is 12 feet..

  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 the Pythagorean Theorem: h=132−52=144=12h=\sqrt{13^2-5^2}=\sqrt{144}=12.
  3. Check the result: The correct answer is 12 feet..

Use the Pythagorean Theorem: h=132−52=144=12h=\sqrt{13^2-5^2}=\sqrt{144}=12.

5. QuestionMultiple choice

An airplane has a 30° angle of depression to a point 100 meters away horizontally. What is the vertical difference?

Please select an answer first.

Correct answer: A

The correct answer is 10033\frac{100\sqrt{3}}{3} meters..

  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: vertical difference = 100tan⁡30°=1003/3100\tan30°=100\sqrt{3}/3.
  3. Check the result: The correct answer is 10033\frac{100\sqrt{3}}{3} meters..

Use tangent: vertical difference = 100tan⁡30°=1003/3100\tan30°=100\sqrt{3}/3.

6. QuestionMultiple choice

A tree casts an 8-meter shadow when the sun angle of elevation is 60°. What is the tree height?

Please select an answer first.

Correct answer: B

The correct answer is 838\sqrt{3} meters..

  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: height = 8tan⁡60°=838\tan60°=8\sqrt{3}.
  3. Check the result: The correct answer is 838\sqrt{3} meters..

Use tangent: height = 8tan⁡60°=838\tan60°=8\sqrt{3}.

7. QuestionMultiple choice

A 10-foot wheelchair ramp makes a 30° angle with the ground. What vertical rise does it provide?

Please select an answer first.

Correct answer: C

The correct answer is 5 feet..

  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 rise is opposite the angle: 10sin⁡30°=510\sin30°=5 feet.
  3. Check the result: The correct answer is 5 feet..

The rise is opposite the angle: 10sin⁡30°=510\sin30°=5 feet.

8. QuestionMultiple choice

A surveyor is 50 meters from a tower and measures a 60° angle of elevation. What is the tower height?

Please select an answer first.

Correct answer: D

The correct answer is 50350\sqrt{3} meters..

  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: height = 50tan⁡60°=50350\tan60°=50\sqrt{3}.
  3. Check the result: The correct answer is 50350\sqrt{3} meters..

Use tangent: height = 50tan⁡60°=50350\tan60°=50\sqrt{3}.

9. QuestionMultiple choice

A roof section rises 4 feet over a horizontal run of 4 feet. What is its angle of elevation?

Please select an answer first.

Correct answer: A

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: The tangent is 4/4=14/4=1, so the acute angle is 45 degrees.
  3. Check the result: The correct answer is 45°..

The tangent is 4/4=14/4=1, so the acute angle is 45 degrees.

10. QuestionMultiple choice

A rescue line forms a 30° angle with level ground and reaches a platform 60 meters away horizontally. How high is the platform?

Please select an answer first.

Correct answer: B

The correct answer is 20320\sqrt{3} meters..

  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: height = 60tan⁡30°=603/3=20360\tan30°=60\sqrt{3}/3=20\sqrt{3}.
  3. Check the result: The correct answer is 20320\sqrt{3} meters..

Use tangent: height = 60tan⁡30°=603/3=20360\tan30°=60\sqrt{3}/3=20\sqrt{3}.

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