Solving for Missing Sides with the Law of Sines

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| By Thames
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Quizzes Created: 7387 | Total Attempts: 9,527,684
| Questions: 20 | Updated: Nov 11, 2025
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1) In △PQR, ∠P = 42°, ∠Q = 68°, side p = 12. Find q.

Explanation

q = (sin 68° / sin 42°) × 12 ≈ 16.63 → 16.6

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About This Quiz
Solving For Missing Sides With The Law Of Sines - Quiz

Ready to explore how angles and sides work together in non-right triangles? In this quiz, you’ll apply the Law of Sines to find unknown sides and deepen your understanding of trigonometric ratios. You’ll calculate missing measures step by step using angle relationships, compare proportions, and interpret results within real geometric... see morecontexts. By the end, you’ll feel confident solving triangles accurately with the Law of Sines!
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2) In △LMN, ∠L = 40°, ∠N = 75°, side l = 8. Find n.

Explanation

n = (sin 75° / sin 40°) × 8 ≈ 12.02 → 12.0

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3) In △ABC, ∠A = 30°, ∠C = 120°, side a = 7. Find c.

Explanation

c = (sin 120° / sin 30°) × 7 = 7√3 ≈ 12.12 → 12.1

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4) In △XYZ, ∠X = 50°, ∠Y = 70°, side x = 10. Find y.

Explanation

y = (sin 70° / sin 50°) × 10 ≈ 12.27 → 12.3

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5) In △DEF, ∠D = 37°, ∠F = 90°, side d = 6. Find f.

Explanation

f = (sin 90° / sin 37°) × 6 ≈ 9.97 → 10.0

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6) In △RST, ∠R = 32°, ∠S = 120°, side r = 12. Find s.

Explanation

s = (sin 120° / sin 32°) × 12 ≈ 19.61 → 19.6

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7) In △JKL, ∠J = 35°, ∠K = 65°, side j = 9. Find k.

Explanation

k = (sin 65° / sin 35°) × 9 ≈ 14.22 → 14.2

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8) In △OPQ, ∠A = 52°, ∠C = 60°, side a = 10. Find c.

Explanation

c = (sin 60° / sin 52°) × 10 ≈ 10.99 → 11.0

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9) In △UVW, ∠U = 53°, ∠W = 90°, side u = 15. Find w.

Explanation

w = (sin 90° / sin 53°) × 15 ≈ 18.78 → 18.8

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10) In △GHI, ∠G = 40°, ∠H = 80°, side g = 7. Find h.

Explanation

h = (sin 80° / sin 40°) × 7 ≈ 10.72 → 10.7

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11) In △MNO, ∠A = 36°, ∠C = 100°, side a = 5. Find c.

Explanation

c = (sin 100° / sin 36°) × 5 ≈ 8.38 → 8.38

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12) In △QRS, ∠Q = 50°, ∠R = 60°, side q = 14. Find r.

Explanation

r = (sin 60° / sin 50°) × 14 ≈ 15.83 → 15.8

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13) In △TUV, ∠T = 39°, ∠U = 90°, side t = 9. Find u.

Explanation

u = (sin 90° / sin 39°) × 9 ≈ 14.30 → 14.3

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14) In △XYZ, ∠X = 30°, ∠Y = 105°, side x = 8. Find y.

Explanation

y = (sin 105° / sin 30°) × 8 ≈ 15.45 → 15.5

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15) In △ABC, ∠A = 28°, ∠C = 120°, side a = 13. Find c.

Explanation

c = (sin 120° / sin 28°) × 13 ≈ 23.98 → 24.0

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16) In △DEF, ∠D = 45°, ∠E = 60°, side d = 10. Find e.

Explanation

e = (sin 60° / sin 45°) × 10 ≈ 12.25 → 12.2

Submit
17) In △PQR, ∠P = 33°, ∠R = 110°, side p = 8. Find r.

Explanation

r = (sin 110° / sin 33°) × 8 ≈ 13.80 → 13.8

Submit
18) In △LMN, ∠L = 55°, ∠N = 65°, side l = 9. Find n.

Explanation

n = (sin 65° / sin 55°) × 9 ≈ 9.96 → 10.0

Submit
19) In △UVW, ∠U = 35°, ∠V = 120°, side u = 7. Find v.

Explanation

v = (sin 120° / sin 35°) × 7 ≈ 10.57 → 10.6

Submit
20) In △RST, ∠R = 70°, ∠S = 50°, side r = 11. Find s.

Explanation

s = (sin 50° / sin 70°) × 11 ≈ 8.97 → 9.0

Submit
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In △PQR, ∠P = 42°, ∠Q = 68°, side p = 12. Find q.
In △LMN, ∠L = 40°, ∠N = 75°, side l = 8. Find n.
In △ABC, ∠A = 30°, ∠C = 120°, side a = 7. Find c.
In △XYZ, ∠X = 50°, ∠Y = 70°, side x = 10. Find y.
In △DEF, ∠D = 37°, ∠F = 90°, side d = 6. Find f.
In △RST, ∠R = 32°, ∠S = 120°, side r = 12. Find s.
In △JKL, ∠J = 35°, ∠K = 65°, side j = 9. Find k.
In △OPQ, ∠A = 52°, ∠C = 60°, side a = 10. Find c.
In △UVW, ∠U = 53°, ∠W = 90°, side u = 15. Find w.
In △GHI, ∠G = 40°, ∠H = 80°, side g = 7. Find h.
In △MNO, ∠A = 36°, ∠C = 100°, side a = 5. Find c.
In △QRS, ∠Q = 50°, ∠R = 60°, side q = 14. Find r.
In △TUV, ∠T = 39°, ∠U = 90°, side t = 9. Find u.
In △XYZ, ∠X = 30°, ∠Y = 105°, side x = 8. Find y.
In △ABC, ∠A = 28°, ∠C = 120°, side a = 13. Find c.
In △DEF, ∠D = 45°, ∠E = 60°, side d = 10. Find e.
In △PQR, ∠P = 33°, ∠R = 110°, side p = 8. Find r.
In △LMN, ∠L = 55°, ∠N = 65°, side l = 9. Find n.
In △UVW, ∠U = 35°, ∠V = 120°, side u = 7. Find v.
In △RST, ∠R = 70°, ∠S = 50°, side r = 11. Find s.
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