SOHCAHTOA Quiz: Defining SOHCAHTOA

  • 10th Grade
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| Attempts: 14 | Questions: 20 | Updated: Dec 17, 2025
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1) What does SOH in SOHCAHTOA stand for?

Explanation

SOH means Sine = Opposite/Hypotenuse. Example: if opposite = 3, hypotenuse = 5, then sin(θ) = 3/5 = 0.6.

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About This Quiz
Sohcahtoa Quiz: Defining Sohcahtoa - Quiz

How do right-triangle ratios form the foundation of trigonometry? In this quiz, you’ll revisit SOHCAHTOA and use it to connect angles with side lengths in a variety of right-triangle setups. You’ll practice identifying opposite, adjacent, and hypotenuse sides, selecting the correct ratio, and applying each function to solve for missing... see morevalues. Through clear, guided examples, you’ll build stronger intuition for how sine, cosine, and tangent describe geometric relationships and support real-world applications.
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2) The tangent of an angle is the ratio of the opposite side to the adjacent side.

Explanation

True. Tangent(θ) = Opposite/Adjacent. Example: tan(θ) = 3/4 = 0.75.

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3) If cos(θ) = 12/13, what is sin(θ)?

Explanation

Using sin²(θ) + cos²(θ) = 1 → sin²(θ) = 1 - (12/13)² = 25/169 → sin(θ) = 5/13.

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4) Select all correct SOHCAHTOA relationships.

Explanation

Correct ratios: Sine = Opp/Hyp, Cosine = Adj/Hyp, Tangent = Opp/Adj.

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5) If sin(θ) = 3/5, what is cos(θ)?

Explanation

Using Pythagoras: hypotenuse = 5, opposite = 3 → adjacent = 4 → cos(θ) = 4/5.

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6) Sine and cosine of complementary angles are equal.

Explanation

True. sin(θ) = cos(90° - θ). Example: sin(30°) = cos(60°) = 0.5.

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7) If tan(θ) = 3/4, what is sin(θ)?

Explanation

tan(θ) = 3/4 → hypotenuse = √(3² + 4²) = 5 → sin(θ) = 3/5.

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8) The tangent of an angle equals the opposite divided by the ______ side.

Explanation

Tangent = Opposite/Adjacent, so denominator is 'adjacent'.

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9) Tangent can be greater than 1.

Explanation

True. tan(θ) > 1 when Opp > Adj. Example: tan(60°) = √3 ≈ 1.732.

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10) The sine of an angle equals ______ divided by the hypotenuse.

Explanation

Sine = Opposite/Hypotenuse. The numerator is 'opposite'.

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11) If sin(θ) = 4/5, what is tan(θ)?

Explanation

sin(θ) = 4/5 → Opp = 4, Hyp = 5 → Adj = 3 → tan(θ) = 4/3.

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12) What does CAH in SOHCAHTOA stand for?

Explanation

CAH means Cosine = Adjacent/Hypotenuse. Example: if Adj=4, Hyp=5 → cos(θ)=4/5.

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13) The cosine of an angle equals ______ divided by the hypotenuse.

Explanation

CAH means Cosine = Adjacent/Hypotenuse. The numerator is 'adjacent'.

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14) If sin(θ) = 0.6, find θ.

Explanation

θ = sin⁻¹(0.6) = 36.87°. This matches a 3-4-5 triangle (3/5 = 0.6).

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15) Choose all correct tangent equations.

Explanation

tan(θ) = Opp/Adj and also equals sin(θ)/cos(θ).

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16) If sin(θ) = 5/13, find tan(θ).

Explanation

sin(θ) = 5/13 → Opp = 5, Hyp = 13 → Adj = √(13² - 5²) = 12 → tan(θ) = 5/12.

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17) If cos(θ) = 0.8, find θ.

Explanation

θ = cos⁻¹(0.8) = 36.87°

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18) Select all equations that represent cosine.

Explanation

cos(θ) = Adj/Hyp and equals sin(90° - θ).

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19) If tan(θ) = 1, what is θ?

Explanation

tan(θ) = 1 when Opp = Adj → θ = 45°.

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20) The cosine of an angle is always greater than the sine for acute angles less than 45°.

Explanation

True. For angles opposite, so cos(θ) > sin(θ).

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What does SOH in SOHCAHTOA stand for?
The tangent of an angle is the ratio of the opposite side to the...
If cos(θ) = 12/13, what is sin(θ)?
Select all correct SOHCAHTOA relationships.
If sin(θ) = 3/5, what is cos(θ)?
Sine and cosine of complementary angles are equal.
If tan(θ) = 3/4, what is sin(θ)?
The tangent of an angle equals the opposite divided by the ______...
Tangent can be greater than 1.
The sine of an angle equals ______ divided by the hypotenuse.
If sin(θ) = 4/5, what is tan(θ)?
What does CAH in SOHCAHTOA stand for?
The cosine of an angle equals ______ divided by the hypotenuse.
If sin(θ) = 0.6, find θ.
Choose all correct tangent equations.
If sin(θ) = 5/13, find tan(θ).
If cos(θ) = 0.8, find θ.
Select all equations that represent cosine.
If tan(θ) = 1, what is θ?
The cosine of an angle is always greater than the sine for acute...
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