Law of Sines in Real Life: Application Quiz

1) A surveyor measures ∠A = 42°, ∠B = 68°, and side a = 120 m in a triangular plot. Find side b.

166 m

159 m

160 m

175 m

2) A bridge support forms △LMN with ∠L = 40°, ∠N = 75°, and side l = 8 m. Find side n.

11.2 m

12.0 m

12.8 m

13.6 m

3) A sail has triangular shape △ABC with ∠A = 30°, ∠C = 120°, and side a = 7 m. Find side c.

11.9 m

12.1 m

12.3 m

12.5 m

4) A roof truss forms △XYZ with ∠X = 50°, ∠Y = 70°, and side x = 10 m. Find side y.

12.0 m

12.2 m

12.4 m

12.3 m

5) A flag is hoisted on a triangular mast △DEF with ∠D = 37°, ∠F = 90°, and side d = 6 m. Find side f.

10.0 m

9.8 m

10.2 m

10.4 m

6) A triangular parcel △RST has ∠R = 32°, ∠S = 120°, and side r = 12 m. Find side s.

19.4 m

19.6 m

19.8 m

20.0 m

7) A sign is supported by triangle △JKL with ∠J = 35°, ∠K = 65°, and side j = 9 m. Find side k.

13.9 m

14.0 m

14.1 m

14.2 m

8) A ramp is modeled as △OPQ with ∠O = 52°, ∠Q = 60°, and side o = 10 m. Find side q.

10.8 m

11.0 m

11.2 m

11.4 m

9) A construction scaffold forms △UVW with ∠U = 53°, ∠W = 90°, and side u = 15 m. Find side w.

18.8 m

18.5 m

19.1 m

19.4 m

10) A triangular panel △GHI has ∠G = 40°, ∠H = 80°, and side g = 7 m. Find side h.

10.5 m

10.6 m

10.8 m

10.7 m

11) A triangular beam △MNO has ∠M = 36°, ∠O = 100°, and side m = 5 m. Find side o.

8.25 m

8.38 m

8.51 m

8.64 m

12) A triangular garden △QRS has ∠Q = 50°, ∠R = 60°, and side q = 14 m. Find side r.

15.5 m

15.7 m

15.8 m

16.0 m

13) A tent cross-section △TUV has ∠T = 39°, ∠U = 90°, and side t = 9 m. Find side u.

14.1 m

14.3 m

14.5 m

14.7 m

14) A triangular shade △XYZ has ∠X = 30°, ∠Y = 105°, and side x = 8 m. Find side y.

15.2 m

15.4 m

15.5 m

15.7 m

15) A triangular support △ABC has ∠A = 28°, ∠C = 120°, and side a = 13 m. Find side c.

23.6 m

23.8 m

24.0 m

24.2 m

16) A triangular tile △DEF has ∠D = 45°, ∠E = 60°, and side d = 10 m. Find side e.

12.2 m

12.4 m

12.6 m

12.8 m

17) A triangular lot △PQR has ∠P = 33°, ∠R = 110°, and side p = 8 m. Find side r.

13.6 m

13.8 m

14.0 m

14.2 m

18) A triangular display △LMN has ∠L = 55°, ∠N = 65°, and side l = 9 m. Find side n.

10.0 m

9.7 m

10.3 m

10.6 m

19) A triangular support △UVW has ∠U = 35°, ∠V = 120°, and side u = 7 m. Find side v.

10.4 m

10.6 m

10.8 m

11.0 m

20) A triangular field △RST has ∠R = 70°, ∠S = 50°, and side r = 11 m. Find side s.

8.6 m

9.0 m

9.4 m

9.8 m

Real World Problems

1) A surveyor measures ∠A = 42°, ∠B = 68°, and side a = 120 m in a triangular plot. Find side b.

2)

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2) A bridge support forms △LMN with ∠L = 40°, ∠N = 75°, and side l = 8 m. Find side n.

3) A sail has triangular shape △ABC with ∠A = 30°, ∠C = 120°, and side a = 7 m. Find side c.

4) A roof truss forms △XYZ with ∠X = 50°, ∠Y = 70°, and side x = 10 m. Find side y.

5) A flag is hoisted on a triangular mast △DEF with ∠D = 37°, ∠F = 90°, and side d = 6 m. Find side f.

6) A triangular parcel △RST has ∠R = 32°, ∠S = 120°, and side r = 12 m. Find side s.

7) A sign is supported by triangle △JKL with ∠J = 35°, ∠K = 65°, and side j = 9 m. Find side k.

8) A ramp is modeled as △OPQ with ∠O = 52°, ∠Q = 60°, and side o = 10 m. Find side q.

9) A construction scaffold forms △UVW with ∠U = 53°, ∠W = 90°, and side u = 15 m. Find side w.

10) A triangular panel △GHI has ∠G = 40°, ∠H = 80°, and side g = 7 m. Find side h.

11) A triangular beam △MNO has ∠M = 36°, ∠O = 100°, and side m = 5 m. Find side o.

12) A triangular garden △QRS has ∠Q = 50°, ∠R = 60°, and side q = 14 m. Find side r.

13) A tent cross-section △TUV has ∠T = 39°, ∠U = 90°, and side t = 9 m. Find side u.

14) A triangular shade △XYZ has ∠X = 30°, ∠Y = 105°, and side x = 8 m. Find side y.

15) A triangular support △ABC has ∠A = 28°, ∠C = 120°, and side a = 13 m. Find side c.

16) A triangular tile △DEF has ∠D = 45°, ∠E = 60°, and side d = 10 m. Find side e.

17) A triangular lot △PQR has ∠P = 33°, ∠R = 110°, and side p = 8 m. Find side r.

18) A triangular display △LMN has ∠L = 55°, ∠N = 65°, and side l = 9 m. Find side n.

19) A triangular support △UVW has ∠U = 35°, ∠V = 120°, and side u = 7 m. Find side v.

20) A triangular field △RST has ∠R = 70°, ∠S = 50°, and side r = 11 m. Find side s.