Apply the Ratio

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1) If sin θ = 2/5 for an acute angle θ, what is the length of the hypotenuse?

Explanation

A sine of 2/5 means “opposite 2 over hypotenuse 5,” so the hypotenuse is 5.

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About This Quiz
Apply The Ratio - Quiz

Can you go beyond recognition and actually apply trig ratios to solve problems? In this quiz, you’ll use sine, cosine, and tangent to find missing side lengths in right triangles. We bring you this quiz so you can practice turning ratios into real answers—step by step, calculation by calculation. Try... see morethis quiz to see how trigonometry works in action! see less

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2) If cos θ = 3/5, what is the length of the hypotenuse?

Explanation

A cosine of 3/5 means “adjacent 3 over hypotenuse 5,” so the hypotenuse is 5.

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3) If tan θ = 5/12, what is the length of the opposite side?

Explanation

A tangent of 5/12 uses “opposite over adjacent,” so the opposite side is 5.

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4) If sin θ = 7/25, what is the length of the opposite side?

Explanation

A sine of 7/25 uses “opposite over hypotenuse,” so the opposite side is 7

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5) If cos θ = 8/17, what is the length of the adjacent side?

Explanation

A cosine of 8/17 uses “adjacent over hypotenuse,” so the adjacent side is 8.

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6) If tan θ = 9/40, what is the opposite side?

Explanation

A tangent of 9/40 uses “opposite over adjacent,” so the opposite side is 9.

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7) If sin θ = 12/13, what is the length of the opposite side?

Explanation

A sine of 12/13 uses “opposite over hypotenuse,” so the opposite side is 12.

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8) If cos θ = 15/17, what is the adjacent side length?

Explanation

A cosine of 15/17 uses “adjacent over hypotenuse,” so the adjacent side is 15.

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9) If sin θ = 3/5, what is the hypotenuse?

Explanation

A sine of 3/5 uses “opposite over hypotenuse,” so the hypotenuse is 5.

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10) If tan θ = 7/24, what is the adjacent side length?

Explanation

A tangent of 7/24 uses “opposite over adjacent,” so the adjacent side is 24.

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11) If cos θ = 4/5, find the opposite side length.

Explanation

A cosine of 4/5 fits the 3–4–5 triangle, so the opposite side is 3.

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12) If sin θ = 5/13, what is the adjacent side length?

Explanation

A sine of 5/13 fits the 5–12–13 triangle, so the adjacent side is 12.

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13) If tan θ = 15/8, what is the length of the hypotenuse?

Explanation

A tangent of 15/8 fits the 8–15–17 triangle, so the hypotenuse is 17.

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14) If cos θ = 9/41, what is the length of the opposite side?

Explanation

A cosine of 9/41 has adjacent 9 and hypotenuse 41, so the opposite side is: 40.

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15) If sin θ = 20/29, what is the adjacent side?

Explanation

A sine of 20/29 has opposite 20 and hypotenuse 29, so the adjacent side is 21.

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16) If tan θ = 5/12 what is the length of the hypotenuse?

Explanation

A tangent of 5/12 fits the 5–12–13 triangle, so the hypotenuse is 13.

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17) If cos θ = 21/29, what is the length of the opposite side?

Explanation

A cosine of 21/29 has adjacent 21 and hypotenuse 29, so the opposite side is 20.

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18) If sin θ = 40/41, what is the length of the adjacent side?

Explanation

A sine of 40/41 has opposite 40 and hypotenuse 41, so the adjacent side is 9.

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19) If tan θ = 12/5, what is the length of the hypotenuse?

Explanation

A tangent of 12/5 uses a 5–12–13 triangle, so the hypotenuse is 13.

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20) If cos θ = 5/13, what is the length of the opposite side?

Explanation

A cosine of 5/13 has adjacent 5 and hypotenuse 13, so the opposite side is 12. 

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If sin θ = 2/5 for an acute angle θ, what is the length of...
If cos θ = 3/5, what is the length of the hypotenuse?
If tan θ = 5/12, what is the length of the opposite side?
If sin θ = 7/25, what is the length of the opposite side?
If cos θ = 8/17, what is the length of the adjacent side?
If tan θ = 9/40, what is the opposite side?
If sin θ = 12/13, what is the length of the opposite side?
If cos θ = 15/17, what is the adjacent side length?
If sin θ = 3/5, what is the hypotenuse?
If tan θ = 7/24, what is the adjacent side length?
If cos θ = 4/5, find the opposite side length.
If sin θ = 5/13, what is the adjacent side length?
If tan θ = 15/8, what is the length of the hypotenuse?
If cos θ = 9/41, what is the length of the opposite side?
If sin θ = 20/29, what is the adjacent side?
If tan θ = 5/12 what is the length of the hypotenuse?
If cos θ = 21/29, what is the length of the opposite side?
If sin θ = 40/41, what is the length of the adjacent side?
If tan θ = 12/5, what is the length of the hypotenuse?
If cos θ = 5/13, what is the length of the opposite side?
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