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Solving Right Triangles with Trigonometry — Easy Worksheet 2
Grade 10 · MathSheets Name: ____________________ Date: __________
Use trigonometric ratios to solve. Round to the nearest tenth.
How to solve
Label the sides relative to θ, then choose the ratio that links the side you know to the side you want: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent (SOH CAH TOA). Solve for the unknown by multiplying or dividing, and round to the nearest tenth.
Example
In a right triangle, angle θ = 70°, and the side opposite θ is 2. Find the length of the side adjacent to θ.
Answer: 0.7
Not quite. The answer is
💡 You know the hypotenuse and want the side opposite θ, so use sine (SOH): sin θ = opposite/hypotenuse. sin 55° = x6. sin 55° ≈ 0.8192, so x = 6 × sin 55° ≈ 4.9149, which rounds to 4.9.
✓ Correct!
Not quite. The answer is
💡 You know the hypotenuse and want the side opposite θ, so use sine (SOH): sin θ = opposite/hypotenuse. sin 55° = x6. sin 55° ≈ 0.8192, so x = 6 × sin 55° ≈ 4.9149, which rounds to 4.9.
💡 How to solve: Solving Right Triangles with Trigonometry
Label the sides relative to θ, then choose the ratio that links the side you know to the side you want: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent (SOH CAH TOA). Solve for the unknown by multiplying or dividing, and round to the nearest tenth.
Try a similar one
In a right triangle, angle θ = 70°, and the side opposite θ is 7. Find the length of the hypotenuse.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 You know the side adjacent to θ and want the side opposite θ, so use tangent (TOA): tan θ = opposite/adjacent. tan 50° = x9. tan 50° ≈ 1.1918, so x = 9 × tan 50° ≈ 10.7258, which rounds to 10.7.
✓ Correct!
Not quite. The answer is
💡 You know the side adjacent to θ and want the side opposite θ, so use tangent (TOA): tan θ = opposite/adjacent. tan 50° = x9. tan 50° ≈ 1.1918, so x = 9 × tan 50° ≈ 10.7258, which rounds to 10.7.
💡 How to solve: Solving Right Triangles with Trigonometry
Label the sides relative to θ, then choose the ratio that links the side you know to the side you want: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent (SOH CAH TOA). Solve for the unknown by multiplying or dividing, and round to the nearest tenth.
Try a similar one
In a right triangle, angle θ = 65°, and the side adjacent to θ is 2. Find the length of the side opposite θ.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 You know the side opposite θ and want the side adjacent to θ, so use tangent (TOA): tan θ = opposite/adjacent. tan 35° = 9x. tan 35° ≈ 0.7002, so x = 9 ÷ tan 35° ≈ 12.8533, which rounds to 12.9.
✓ Correct!
Not quite. The answer is
💡 You know the side opposite θ and want the side adjacent to θ, so use tangent (TOA): tan θ = opposite/adjacent. tan 35° = 9x. tan 35° ≈ 0.7002, so x = 9 ÷ tan 35° ≈ 12.8533, which rounds to 12.9.
💡 How to solve: Solving Right Triangles with Trigonometry
Label the sides relative to θ, then choose the ratio that links the side you know to the side you want: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent (SOH CAH TOA). Solve for the unknown by multiplying or dividing, and round to the nearest tenth.
Try a similar one
In a right triangle, angle θ = 25°, and the side opposite θ is 7. Find the length of the hypotenuse.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 You know the hypotenuse and want the side opposite θ, so use sine (SOH): sin θ = opposite/hypotenuse. sin 30° = x8. sin 30° ≈ 0.5000, so x = 8 × sin 30° ≈ 4, which rounds to 4.0.
✓ Correct!
Not quite. The answer is
💡 You know the hypotenuse and want the side opposite θ, so use sine (SOH): sin θ = opposite/hypotenuse. sin 30° = x8. sin 30° ≈ 0.5000, so x = 8 × sin 30° ≈ 4, which rounds to 4.0.
💡 How to solve: Solving Right Triangles with Trigonometry
Label the sides relative to θ, then choose the ratio that links the side you know to the side you want: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent (SOH CAH TOA). Solve for the unknown by multiplying or dividing, and round to the nearest tenth.
Try a similar one
In a right triangle, angle θ = 20°, and the side adjacent to θ is 8. Find the length of the side opposite θ.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 You know the side opposite θ and want the side adjacent to θ, so use tangent (TOA): tan θ = opposite/adjacent. tan 70° = 9x. tan 70° ≈ 2.7475, so x = 9 ÷ tan 70° ≈ 3.2757, which rounds to 3.3.
✓ Correct!
Not quite. The answer is
💡 You know the side opposite θ and want the side adjacent to θ, so use tangent (TOA): tan θ = opposite/adjacent. tan 70° = 9x. tan 70° ≈ 2.7475, so x = 9 ÷ tan 70° ≈ 3.2757, which rounds to 3.3.
💡 How to solve: Solving Right Triangles with Trigonometry
Label the sides relative to θ, then choose the ratio that links the side you know to the side you want: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent (SOH CAH TOA). Solve for the unknown by multiplying or dividing, and round to the nearest tenth.
Try a similar one
In a right triangle, angle θ = 60°, and the hypotenuse is 5. Find the length of the side adjacent to θ.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 You know the side opposite θ and want the hypotenuse, so use sine (SOH): sin θ = opposite/hypotenuse. sin 60° = 7x. sin 60° ≈ 0.8660, so x = 7 ÷ sin 60° ≈ 8.0829, which rounds to 8.1.
✓ Correct!
Not quite. The answer is
💡 You know the side opposite θ and want the hypotenuse, so use sine (SOH): sin θ = opposite/hypotenuse. sin 60° = 7x. sin 60° ≈ 0.8660, so x = 7 ÷ sin 60° ≈ 8.0829, which rounds to 8.1.
💡 How to solve: Solving Right Triangles with Trigonometry
Label the sides relative to θ, then choose the ratio that links the side you know to the side you want: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent (SOH CAH TOA). Solve for the unknown by multiplying or dividing, and round to the nearest tenth.
Try a similar one
In a right triangle, angle θ = 20°, and the side adjacent to θ is 5. Find the length of the hypotenuse.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 You know the side adjacent to θ and want the side opposite θ, so use tangent (TOA): tan θ = opposite/adjacent. tan 20° = x9. tan 20° ≈ 0.3640, so x = 9 × tan 20° ≈ 3.2757, which rounds to 3.3.
✓ Correct!
Not quite. The answer is
💡 You know the side adjacent to θ and want the side opposite θ, so use tangent (TOA): tan θ = opposite/adjacent. tan 20° = x9. tan 20° ≈ 0.3640, so x = 9 × tan 20° ≈ 3.2757, which rounds to 3.3.
💡 How to solve: Solving Right Triangles with Trigonometry
Label the sides relative to θ, then choose the ratio that links the side you know to the side you want: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent (SOH CAH TOA). Solve for the unknown by multiplying or dividing, and round to the nearest tenth.
Try a similar one
In a right triangle, angle θ = 70°, and the side opposite θ is 5. Find the length of the hypotenuse.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
Not quite. The answer is
💡 You know the side adjacent to θ and want the hypotenuse, so use cosine (CAH): cos θ = adjacent/hypotenuse. cos 35° = 9x. cos 35° ≈ 0.8192, so x = 9 ÷ cos 35° ≈ 10.987, which rounds to 11.0.
✓ Correct!
Not quite. The answer is
💡 You know the side adjacent to θ and want the hypotenuse, so use cosine (CAH): cos θ = adjacent/hypotenuse. cos 35° = 9x. cos 35° ≈ 0.8192, so x = 9 ÷ cos 35° ≈ 10.987, which rounds to 11.0.
💡 How to solve: Solving Right Triangles with Trigonometry
Label the sides relative to θ, then choose the ratio that links the side you know to the side you want: sin θ = opposite ÷ hypotenuse, cos θ = adjacent ÷ hypotenuse, tan θ = opposite ÷ adjacent (SOH CAH TOA). Solve for the unknown by multiplying or dividing, and round to the nearest tenth.
Try a similar one
In a right triangle, angle θ = 65°, and the side adjacent to θ is 6. Find the length of the hypotenuse.
✓ You've got it! Press Next to keep going. Not yet — the answer is . Read the steps above once more.
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Solving Right Triangles with Trigonometry — Easy Worksheet 2
Use trigonometric ratios to solve. Round to the nearest tenth.