Find Missing Sides with Sine, Cosine, & Tangent

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| Questions: 20 | Updated: Nov 10, 2025
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1) In a right triangle, angle A = 30°. If the hypotenuse is 12, find the side opposite A.

Explanation

opposite = hypotenuse × sin 30° = 12 × (1/2) = 6. Hence, opposite = 6.

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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 trig functions connect angles and side lengths, preparing you for real-world geometry and problem-solving in physics and design. see less

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

Explanation

cos 45° = adjacent / hypotenuse = 10 / H; H = 10 / (√2/2) = 10√2. Hence, hypotenuse = 10√2.

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

Explanation

cos 60° = adjacent / hypotenuse = 5 / H; H = 5 / 0.5 = 10. Hence, hypotenuse = 10.0.

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

Explanation

other² = 13² − 5² = 169 − 25 = 144; other = √144 = 12. Hence, the other leg = 12.

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

Explanation

tan θ = opposite / adjacent = 3/4; opposite = (3/4) × 8 = 6. Hence, opposite = 6.

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

Explanation

adjacent² = 25² − 7² = 625 − 49 = 576; adjacent = √576 = 24. Hence, adjacent = 24.

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

Explanation

sin 37° = opposite / hypotenuse = 9 / H; H = 9 / sin 37° ≈ 9 / 0.6018 ≈ 15.0. Hence, hypotenuse ≈ 15.0.

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

Explanation

hypotenuse = √(9² + 12²) = 15; sin θ = opposite / hypotenuse = 12 / 15 = 0.80. Hence, sin θ = 0.80.

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9) Cos θ = 5/13. Find sin θ.

Explanation

sin θ = √(1 − cos²θ) = √(1 − (5/13)²) = √(144/169) = 12/13. Hence, sin θ = 12/13.

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

Explanation

adjacent = hypotenuse × cos 53° ≈ 20 × 0.6018 = 12.0. Hence, adjacent ≈ 12.0.

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

Explanation

hypotenuse = opposite / sin 40° = 8 / 0.6428 ≈ 12.4. Hence, hypotenuse ≈ 12.4.

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

Explanation

adjacent = hypotenuse × cos 65° ≈ 30 × 0.4226 = 12.7. Hence, adjacent ≈ 12.7.

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

Explanation

opposite² = 25² − 15² = 625 − 225 = 400; opposite = √400 = 20. Hence, opposite = 20.

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14) Sin α = 7/25. Find cos α.

Explanation

cos α = √(1 − sin²α) = √(1 − (7/25)²) = √(576/625) = 24/25. Hence, cos α = 24/25.

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

Explanation

opposite = adjacent × tan 28° ≈ 14 × 0.5317 = 7.4. Hence, opposite ≈ 7.4.

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

Explanation

opposite = hypotenuse × sin 45° = 10 × (√2/2) = 7.1. Hence, opposite ≈ 7.1.

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

Explanation

tan β = opposite / adjacent = 2/5; adjacent = opposite × (5/2) = 8 × 2.5 = 20. Hence, adjacent = 20.

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

Explanation

opposite² = 50² − 30² = 1600; opposite = 40; sin θ = opposite / hypotenuse = 40 / 50 = 0.80.

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19) Angle = 25°, adjacent = 100. Find opposite (nearest tenth).

Explanation

opposite = adjacent × tan 25° ≈ 100 × 0.4663 = 46.6. Hence, opposite ≈ 46.6.

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

Explanation

tan θ = 4/10 = 0.4; θ = arctan(0.4) ≈ 21.8°; nearest degree: 22°. Hence, θ ≈ 22°.

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In a right triangle, angle A = 30°. If the hypotenuse is 12, find...
In a right triangle, angle B = 45° and adjacent side = 10. Find the...
Angle θ = 60°, adjacent = 5. Find the hypotenuse.
A right triangle has hypotenuse 13 and one leg 5. Find the other leg.
Tan θ = 3/4, adjacent = 8. Find the opposite side.
Opposite = 7, hypotenuse = 25. Find the adjacent side.
Angle C = 37°, opposite = 9. Find the hypotenuse (nearest tenth).
Adjacent = 9, opposite = 12. Find sin θ.
Cos θ = 5/13. Find sin θ.
Angle A = 53°, hypotenuse = 20. Find the adjacent side (nearest...
Opposite = 8, θ = 40°. Find the hypotenuse (nearest tenth).
Angle B = 65°, hypotenuse = 30. Find the adjacent side (nearest...
Hypotenuse = 25, adjacent = 15. Find the opposite side.
Sin α = 7/25. Find cos α.
Angle θ = 28°, adjacent = 14. Find the opposite side (nearest...
Hypotenuse = 10, angle = 45°. Find the opposite side (nearest tenth).
Tan β = 2/5, opposite = 8. Find the adjacent side.
Hypotenuse = 50, adjacent = 30. Find sin θ.
Angle = 25°, adjacent = 100. Find opposite (nearest tenth).
In a right triangle, the ratio of rise to run is 4:10. Find the angle...
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