Trigonometric Ratios Quiz

Grade 10 · Math · Quiz

Test your ability to apply sine, cosine, and tangent to solve right triangle problems.

Questions

  1. In a right triangle, the sine of an angle is defined as:

    1. adjacent / hypotenuse
    2. opposite / adjacent
    3. opposite / hypotenuse
    4. hypotenuse / opposite
    Show answer

    Answer: opposite / hypotenuse

    Sine = opposite / hypotenuse. SOH in the mnemonic SOH-CAH-TOA stands for Sine = Opposite over Hypotenuse.

  2. A right triangle has a leg of 5 and hypotenuse of 13. What is the sine of the angle opposite the leg of 5?

    1. 5/12
    2. 12/13
    3. 5/13
    4. 13/5
    Show answer

    Answer: 5/13

    The missing leg is √(13²-5²) = √(169-25) = √144 = 12. The angle opposite the leg of 5 has sin = 5/13.

  3. Which ratio equals the tangent of angle A in a right triangle?

    1. sin A / cos A
    2. cos A / sin A
    3. 1 / sin A
    4. 1 / cos A
    Show answer

    Answer: sin A / cos A

    tan A = opposite/adjacent = (opposite/hypotenuse) / (adjacent/hypotenuse) = sin A / cos A.

  4. The cosine of an angle in a right triangle can ever be greater than 1.

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    Answer: False

    Cosine equals adjacent/hypotenuse. The adjacent side can never exceed the hypotenuse (the longest side), so cosine is always between 0 and 1 for acute angles.

  5. A ramp rises 3 meters over a horizontal distance of 4 meters. What is the tangent of the angle the ramp makes with the ground?

    1. 4/5
    2. 3/5
    3. 3/4
    4. 4/3
    Show answer

    Answer: 3/4

    Tangent = opposite/adjacent = 3/4. The hypotenuse (5) is not used for tangent.

  6. The mnemonic SOH-CAH-TOA helps remember that cosine equals adjacent divided by ___.

    Show answer

    Answer: hypotenuse

    CAH stands for Cosine = Adjacent over Hypotenuse. The denominator is always the hypotenuse.

  7. If sin θ = 0.6 and θ is an acute angle, what is cos θ?

    1. 0.4
    2. 0.8
    3. 0.6
    4. 1.0
    Show answer

    Answer: 0.8

    Using the Pythagorean identity sin²θ + cos²θ = 1: 0.36 + cos²θ = 1, so cos²θ = 0.64, and cos θ = 0.8.

  8. A surveyor stands 50 m from a building and measures the angle of elevation to the top as 60°. Using tan 60° ≈ 1.73, approximately how tall is the building?

    1. 28.9 m
    2. 50 m
    3. 86.5 m
    4. 100 m
    Show answer

    Answer: 86.5 m

    tan 60° = height/50, so height = 50 × 1.73 = 86.5 m.

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