Let’s solve each right triangle problem one by one. We’ll use trigonometry (sine, cosine, tangent) and the Pythagorean theorem where needed. All answers will be rounded to the nearest tenth.
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Problem 1:
Given: angle = 30°, adjacent side = 48, find opposite side (x)
Use tangent:
tan(θ) = opposite / adjacent
tan(30°) = x / 48
x = 48 × tan(30°)
tan(30°) ≈ 0.5774
x ≈ 48 × 0.5774 ≈ 27.7
✔ Answer for #1: x ≈ 27.7
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Problem 2:
Given: angle = 62°, hypotenuse = 19, find adjacent side (x)
Use cosine:
cos(θ) = adjacent / hypotenuse
cos(62°) = x / 19
x = 19 × cos(62°)
cos(62°) ≈ 0.4695
x ≈ 19 × 0.4695 ≈ 8.9
✔ Answer for #2: x ≈ 8.9
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Problem 3:
Given: angle = 52°, opposite side = 20, find hypotenuse (x)
Use sine:
sin(θ) = opposite / hypotenuse
sin(52°) = 20 / x
x = 20 / sin(52°)
sin(52°) ≈ 0.7880
x ≈ 20 / 0.7880 ≈ 25.4
✔ Answer for #3: x ≈ 25.4
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Problem 4:
Given: angle = 55°, adjacent side = 16, find hypotenuse (x)
Use cosine:
cos(55°) = adjacent / hypotenuse = 16 / x
x = 16 / cos(55°)
cos(55°) ≈ 0.5736
x ≈ 16 / 0.5736 ≈ 27.9
✔ Answer for #4: x ≈ 27.9
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Problem 5:
Given: angle = 25°, opposite side = 21, find adjacent side (x)
Use tangent:
tan(25°) = opposite / adjacent = 21 / x
x = 21 / tan(25°)
tan(25°) ≈ 0.4663
x ≈ 21 / 0.4663 ≈ 45.0
✔ Answer for #5: x ≈ 45.0
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Problem 6:
Given: angle = 58°, hypotenuse = 13, find opposite side (x)
Use sine:
sin(58°) = opposite / hypotenuse = x / 13
x = 13 × sin(58°)
sin(58°) ≈ 0.8480
x ≈ 13 × 0.8480 ≈ 11.0
✔ Answer for #6: x ≈ 11.0
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Problem 7:
Given: two legs are 5 and 12, find hypotenuse (x) — this is a right triangle with no angles given, so use Pythagorean theorem.
a² + b² = c²
5² + 12² = x²
25 + 144 = x²
169 = x²
x = √169 = 13.0
✔ Answer for #7: x = 13.0
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Problem 8:
Given: angle = 35°, adjacent side = 12, find opposite side (x)
Use tangent:
tan(35°) = x / 12
x = 12 × tan(35°)
tan(35°) ≈ 0.7002
x ≈ 12 × 0.7002 ≈ 8.4
✔ Answer for #8: x ≈ 8.4
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Problem 9:
Given: two legs are 10 and 10, find hypotenuse (x) — again, use Pythagorean theorem.
10² + 10² = x²
100 + 100 = x²
200 = x²
x = √200 ≈ 14.142 → round to 14.1
✔ Answer for #9: x ≈ 14.1
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Problem 10:
Given: angle = 30°, hypotenuse = 20, find adjacent side (x)
Use cosine:
cos(30°) = x / 20
x = 20 × cos(30°)
cos(30°) ≈ 0.8660
x ≈ 20 × 0.8660 ≈ 17.3
✔ Answer for #10: x ≈ 17.3
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Final Answer:
1. 27.7
2. 8.9
3. 25.4
4. 27.9
5. 45.0
6. 11.0
7. 13.0
8. 8.4
9. 14.1
10. 17.3
Parent Tip: Review the logic above to help your child master the concept of right triangle worksheet.
