Find Missing Sides with Sine, Cosine, & Tangent

9th Grade

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Quizzes Created: 7682 | Total Attempts: 9,547,133

| Attempts: 15 | Questions: 20 | Updated: Dec 11, 2025

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1) Opposite = 7, hypotenuse = 25. Find the adjacent side.

Use the Pythagorean theorem:

adjacent² = hypotenuse² − opposite²

So:

adjacent² = 25² − 7² = 625 − 49 = 576

Take the square root:

adjacent = √576 = 24

Hence, the adjacent side = 24.

Explanation

Submit

About This Quiz

Find Missing Sides With Sine, Cosine, & Tangent - Quiz

Get ready to put trigonometry into action. In this quiz, you will use sine, cosine, and tangent to find unknown sides in right triangles. Each problem gives you one or more sides and an angle, and you’ll apply the correct trig ratio to calculate the missing length. This quiz strengthens... see moreyour understanding of how trignometric functions connect angles and side lengths, preparing you for real-world geometry and problem-solving in physics and design.
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2) What first name or nickname would you like us to use?

You may optionally provide this to label your report, leaderboard, or certificate.

2) Angle C = 37°, opposite = 9. Find the hypotenuse (nearest tenth).

13.2

16.8

Use the sine ratio:

sin 37° = opposite / hypotenuse = 9 / H

Solve for H:

H = 9 / sin 37° ≈ 9 / 0.6018 ≈ 15.0

Hence, the hypotenuse ≈ 15.0.

Explanation

Use the sine ratio:

sin 37° = opposite / hypotenuse = 9 / H

Solve for H:

H = 9 / sin 37° ≈ 9 / 0.6018 ≈ 15.0

Hence, the hypotenuse ≈ 15.0.

Submit

3) Opposite = 8, θ = 40°. Find the hypotenuse (nearest tenth).

10.8

12.4

11.9

13.7

Use the sine ratio:

hypotenuse = opposite / sin θ

So:

hypotenuse = 8 / sin 40° ≈ 8 / 0.6428 ≈ 12.4

Hence, hypotenuse ≈ 12.4.

Explanation

Use the sine ratio:

hypotenuse = opposite / sin θ

So:

hypotenuse = 8 / sin 40° ≈ 8 / 0.6428 ≈ 12.4

Hence, hypotenuse ≈ 12.4.

Submit

4) Hypotenuse = 25, adjacent = 15. Find the opposite side.

17.8

21.5

Use the Pythagorean theorem:

opposite² = 25² − 15² = 625 − 225 = 400

Take the square root:

opposite = √400 = 20

Hence, the opposite side = 20.

Explanation

Use the Pythagorean theorem:

opposite² = 25² − 15² = 625 − 225 = 400

Take the square root:

opposite = √400 = 20

Hence, the opposite side = 20.

Submit

5) Sin α = 7/25. Find cos α.

20/25

18/25

24/25

15/25

Use the identity:

cos α = √(1 − sin²α)

Substitute sin α = 7/25:

cos α = √(1 − (7/25)²)

= √(1 − 49/625)

= √(576/625)

= 24/25

Hence, cos α = 24/25.

Explanation

Use the identity:

cos α = √(1 − sin²α)

Substitute sin α = 7/25:

cos α = √(1 − (7/25)²)

= √(1 − 49/625)

= √(576/625)

= 24/25

Hence, cos α = 24/25.

Submit

6) In a right triangle, the ratio of rise to run is 4:10. Find the angle θ (nearest degree).

21°

22°

23°

25°

The rise/run ratio gives:

tan θ = 4 / 10 = 0.4

Now find the angle:

θ = arctan(0.4) ≈ 21.8°

Rounded to the nearest degree:

θ ≈ 22°

Hence, θ ≈ 22°.

Explanation

The rise/run ratio gives:

tan θ = 4 / 10 = 0.4

Now find the angle:

θ = arctan(0.4) ≈ 21.8°

Rounded to the nearest degree:

θ ≈ 22°

Hence, θ ≈ 22°.

Submit

7) In a right triangle, angle A = 30°. If the hypotenuse is 12, find the side opposite A.

4√3

6√3

Use the sine ratio:

opposite = hypotenuse × sin 30°

So, substitute the values:

opposite = 12 × sin 30°

sin 30° = 1/2

Thus:

opposite = 12 × (1/2) = 6

Hence, the opposite side = 6.

Explanation

Use the sine ratio:

opposite = hypotenuse × sin 30°

So, substitute the values:

opposite = 12 × sin 30°

sin 30° = 1/2

Thus:

opposite = 12 × (1/2) = 6

Hence, the opposite side = 6.

Submit

8) In a right triangle, angle B = 45° and adjacent side = 10. Find the hypotenuse.

10√2

8√2

Use the cosine ratio:

cos 45° = adjacent / hypotenuse = 10 / H

Solve for H:

H = 10 / cos 45°

cos 45° = √2/2

So:

H = 10 / (√2/2) = 10√2

Hence, the hypotenuse = 10√2.

Explanation

Use the cosine ratio:

cos 45° = adjacent / hypotenuse = 10 / H

Solve for H:

H = 10 / cos 45°

cos 45° = √2/2

So:

H = 10 / (√2/2) = 10√2

Hence, the hypotenuse = 10√2.

Submit

9) Angle θ = 60°, adjacent = 5. Find the hypotenuse.

8.5

Use the cosine ratio:

cos 60° = adjacent / hypotenuse = 5 / H

Solve for H:

H = 5 / cos 60°

cos 60° = 0.5

So:

H = 5 / 0.5 = 10

Hence, the hypotenuse = 10.

Explanation

Use the cosine ratio:

cos 60° = adjacent / hypotenuse = 5 / H

Solve for H:

H = 5 / cos 60°

cos 60° = 0.5

So:

H = 5 / 0.5 = 10

Hence, the hypotenuse = 10.

Submit

10) A right triangle has hypotenuse 13 and one leg 5. Find the other leg.

Use the Pythagorean theorem:

other² = hypotenuse² − leg²

So:

other² = 13² − 5² = 169 − 25 = 144

Take the square root:

other = √144 = 12

Hence, the other leg = 12.

Explanation

Use the Pythagorean theorem:

other² = hypotenuse² − leg²

So:

other² = 13² − 5² = 169 − 25 = 144

Take the square root:

other = √144 = 12

Hence, the other leg = 12.

Submit

11) Tan θ = 3/4, adjacent = 8. Find the opposite side.

Use the tangent ratio:

tan θ = opposite / adjacent = 3/4

So, opposite = (3/4) × 8 = 6

Hence, the opposite side = 6.

Explanation

Use the tangent ratio:

tan θ = opposite / adjacent = 3/4

So, opposite = (3/4) × 8 = 6

Hence, the opposite side = 6.

Submit

12) Adjacent = 9, opposite = 12. Find sin θ.

0.8

0.6

0.7

0.75

First find the hypotenuse:

hypotenuse = √(9² + 12²) = √(81 + 144) = √225 = 15

Then use the sine ratio:

sin θ = opposite / hypotenuse = 12 / 15 = 0.80

Hence, sin θ = 0.80.

Explanation

First find the hypotenuse:

hypotenuse = √(9² + 12²) = √(81 + 144) = √225 = 15

Then use the sine ratio:

sin θ = opposite / hypotenuse = 12 / 15 = 0.80

Hence, sin θ = 0.80.

Submit

13) Cos θ = 5/13. Find sin θ.

10/13

12/13

11/13

9/13

Use the identity:

sin²θ + cos²θ = 1

So:

sin θ = √(1 − cos²θ)

= √(1 − (5/13)²)

= √(1 − 25/169)

= √(144/169) = 12/13

Hence, sin θ = 12/13.

Explanation

Use the identity:

sin²θ + cos²θ = 1

So:

sin θ = √(1 − cos²θ)

= √(1 − (5/13)²)

= √(1 − 25/169)

= √(144/169) = 12/13

Hence, sin θ = 12/13.

Submit

14) Angle A = 53°, hypotenuse = 20. Find the adjacent side (nearest tenth).

11.4

14.1

Use the cosine ratio:

adjacent = hypotenuse × cos 53°

Substitute values:

adjacent ≈ 20 × 0.6018 ≈ 12.0

Hence, the adjacent side ≈ 12.0.

Explanation

Use the cosine ratio:

adjacent = hypotenuse × cos 53°

Substitute values:

adjacent ≈ 20 × 0.6018 ≈ 12.0

Hence, the adjacent side ≈ 12.0.

Submit

15) Angle B = 65°, hypotenuse = 30. Find the adjacent side (nearest tenth).

12.7

13.1

11.5

Use the cosine ratio:

adjacent = hypotenuse × cos 65°

Substitute values:

adjacent ≈ 30 × 0.4226 ≈ 12.7

Hence, adjacent ≈ 12.7.

Explanation

Use the cosine ratio:

adjacent = hypotenuse × cos 65°

Substitute values:

adjacent ≈ 30 × 0.4226 ≈ 12.7

Hence, adjacent ≈ 12.7.

Submit

16) Angle θ = 28°, adjacent = 14. Find the opposite side (nearest tenth).

6.9

7.1

7.3

7.4

Use the tangent ratio:

opposite = adjacent × tan 28°

Compute:

opposite ≈ 14 × 0.5317 ≈ 7.4

Hence, opposite ≈ 7.4.

Explanation

Use the tangent ratio:

opposite = adjacent × tan 28°

Compute:

opposite ≈ 14 × 0.5317 ≈ 7.4

Hence, opposite ≈ 7.4.

Submit

17) Hypotenuse = 10, angle = 45°. Find the opposite side (nearest tenth).

6.9

7.1

7.2

7.5

Use the sine ratio:

opposite = hypotenuse × sin 45°

sin 45° = √2/2

Thus:

opposite = 10 × (√2/2) = 7.07 ≈ 7.1

Hence, opposite ≈ 7.1.

Explanation

Use the sine ratio:

opposite = hypotenuse × sin 45°

sin 45° = √2/2

Thus:

opposite = 10 × (√2/2) = 7.07 ≈ 7.1

Hence, opposite ≈ 7.1.

Submit

18) Tan β = 2/5, opposite = 8. Find the adjacent side.

Use the tangent ratio:

tan β = opposite / adjacent = 2/5

Solve for adjacent:

adjacent = opposite × (5/2)

adjacent = 8 × 2.5 = 20

Hence, adjacent = 20.

Explanation

Use the tangent ratio:

tan β = opposite / adjacent = 2/5

Solve for adjacent:

adjacent = opposite × (5/2)

adjacent = 8 × 2.5 = 20

Hence, adjacent = 20.

Submit

19) Hypotenuse = 50, adjacent = 30. Find sin θ.

0.6

0.7

0.8

0.5

Use the Pythagorean theorem:

opposite² = hypotenuse² − adjacent²

Compute:

opposite² = 50² − 30² = 2500 − 900 = 1600

opposite = √1600 = 40

Then:

sin θ = opposite / hypotenuse = 40 / 50 = 0.80

Hence, sin θ = 0.80.

Explanation