Finding Angles with Trigonometric Ratios

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| Questions: 20 | Updated: Nov 11, 2025
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1) A right triangle has opposite = 9 and adjacent = 12. Find θ to the nearest degree.

Explanation

θ = arctan(9/12) ≈ 36.87° → 36°.

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About This Quiz
Finding Angles With Trigonometric Ratios - Quiz

Ready to connect triangles to real-world scenarios? In this quiz, you’ll use sine, cosine, and tangent to find unknown angles and sides in right triangles. You’ll explore how trigonometric ratios help solve problems involving ladders, ramps, shadows, and buildings. Step by step, you’ll build accuracy and confidence in applying trig... see moreratios to everyday geometry challenges!
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2) A ladder 10 ft long leans against a wall. The base is 6 ft from the wall. Find the angle of elevation to the nearest degree.

Explanation

cosθ = 6/10 → θ = arccos(0.6) ≈ 53.13° → 53°.

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3) A right triangle has legs 7 and 24. Find the hypotenuse.

Explanation

Hypotenuse = √(7² + 24²) = 25.

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4) A ramp rises 2 m over a run of 5 m. Find the angle of elevation to the nearest degree.

Explanation

θ = arctan(2/5) ≈ 21.80° → 21°.

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

Explanation

Other leg = √(13² − 5²) = √144 = 12.

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6) A building casts a 20 m shadow. If the sun’s angle of elevation is 40°, find the height of the building.

Explanation

Height = 20·tan40° ≈ 16.78 m → 16.8 m.

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7) A right triangle has opposite = 8, hypotenuse = 17. Find θ to the nearest degree.

Explanation

sinθ = 8/17 → θ ≈ 28.1° → 28°.

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8) A ladder 15 ft long leans so it makes a 60° angle with the ground. How high does it reach?

Explanation

Height = 15·sin60° ≈ 12.99 ft → 13.0 ft.

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9) A right triangle has adjacent = 7 and hypotenuse = 25. Find θ to the nearest degree.

Explanation

cosθ = 7/25 → θ ≈ 73.74° → 74°.

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10) A 12 m tall pole casts a shadow of 5 m. Find the angle of elevation of the sun to the nearest degree.

Explanation

θ = arctan(12/5) ≈ 67.38° → 67°.

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11) A right triangle has legs 9 and 40. Find the hypotenuse.

Explanation

Using Pythagoras: √(9² + 40²) = 41. Correct answer is 41.

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12) A 20 m ladder makes a 75° angle with the ground. How high up the wall does it reach?

Explanation

Height = 20 × sin(75°) = 19.3 m. Correct answer is 19.3 m.

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13) A right triangle has opposite = 15, adjacent = 20. Find θ to the nearest degree.

Explanation

θ = tan⁻¹(15/20) = 36.9°, approximately 37°.

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14) A right triangle has hypotenuse 29 and one leg 21. Find the other leg.

Explanation

Other leg = √(29² - 21²) = 20. Correct answer is 20.

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15) A tree casts a 30 ft shadow. If the sun’s angle of elevation is 55°, find the height of the tree.

Explanation

Height = 30 × tan(55°) = 42.8 ft. Correct answer is 42.8 ft.

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16) A right triangle has opposite = 5, hypotenuse = 13. Find θ to the nearest degree.

Explanation

θ = sin⁻¹(5/13) = 22.6°, approximately 23°.

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17) A ladder 25 ft long leans so it reaches 24 ft up a wall. Find the angle with the ground to the nearest degree.

Explanation

θ = sin⁻¹(24/25) = 73.7°, approximately 74°.

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18) A right triangle has adjacent = 9, hypotenuse = 15. Find θ to the nearest degree.

Explanation

θ = cos⁻¹(9/15) = 53.1°, approximately 53°.

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19) A right triangle has opposite = 10, adjacent = 10. Find θ.

Explanation

θ = tan⁻¹(10/10) = 45.0°. Correct answer is 45°.

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20) A ramp is 12 ft long and rises 7 ft. Find the angle of elevation to the nearest degree.

Explanation

θ = sin⁻¹(7/12) = 35.7°, approximately 35°.

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A right triangle has opposite = 9 and adjacent = 12. Find θ to the...
A ladder 10 ft long leans against a wall. The base is 6 ft from the...
A right triangle has legs 7 and 24. Find the hypotenuse.
A ramp rises 2 m over a run of 5 m. Find the angle of elevation to the...
A right triangle has hypotenuse 13 and one leg 5. Find the other leg.
A building casts a 20 m shadow. If the sun’s angle of elevation is...
A right triangle has opposite = 8, hypotenuse = 17. Find θ to the...
A ladder 15 ft long leans so it makes a 60° angle with the ground....
A right triangle has adjacent = 7 and hypotenuse = 25. Find θ to the...
A 12 m tall pole casts a shadow of 5 m. Find the angle of elevation of...
A right triangle has legs 9 and 40. Find the hypotenuse.
A 20 m ladder makes a 75° angle with the ground. How high up the wall...
A right triangle has opposite = 15, adjacent = 20. Find θ to the...
A right triangle has hypotenuse 29 and one leg 21. Find the other leg.
A tree casts a 30 ft shadow. If the sun’s angle of elevation is...
A right triangle has opposite = 5, hypotenuse = 13. Find θ to the...
A ladder 25 ft long leans so it reaches 24 ft up a wall. Find the...
A right triangle has adjacent = 9, hypotenuse = 15. Find θ to the...
A right triangle has opposite = 10, adjacent = 10. Find θ.
A ramp is 12 ft long and rises 7 ft. Find the angle of elevation to...
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