Solving for Missing Sides with the Law of Sines

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Attempts: 13 | Questions: 20 | Updated: Jan 21, 2026
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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

Submit

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

Explanation

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

Submit

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

Explanation

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

Submit

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

Explanation

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

Submit

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

Explanation

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

Submit

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

Explanation

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

Submit

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

Explanation

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

Submit

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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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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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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