MCR3UI Date: _________________________ 1. Determine the number of possible triangles that could be drawn with the given measures. Then, find the measures of the other angles in each possible triangle. Round to the nearest tenth of a degree, if necessary. a) ∆ABC, where ∠A = 42°, a = 30 cm and b = 25 cm b) ∆ABC, where ∠B = 27°, b = 25 cm and c = 30 cm c) ∆PQR, where ∠P = 30°, p = 24 cm and q = 48 cm d) ∆KLM, where ∠M = 37.3°, m = 85 cm and l = 90 cm e) ∆UVW, where ∠W = 38.7°, w = 10 cm and v = 25 cm f) ∆ABC, where ∠B = 48°, c = 15.6 m and b = 12.6 m g) ∆XYZ, where ∠X = 120°, x = 40 cm and z = 20 cm h) ∆DEF, where ∠E = 144°, e = 10.5 m and f = 12.5 m 2. Solve each triangle. Round the angle measures to the nearest tenth of a degree and the side length to the nearest tenth of a centimeter, if necessary. a) ∆ABC, where ∠A = 45°, a = 30 cm and b = 24 cm b) ∆PQR, where ∠R = 40.3°, r = 35.2 cm and q = 40.5 cm c) ∆RST, where ∠T = 50.2°, s = 10.5 cm and t = 7.1 cm Answers 2a) one, ∠B = 33.9°, ∠C = 104.1° 2b) two, ∠A = 6.0°, ∠C = 147.0° or ∠A = 120.0°, ∠C = 33.0° 2c) one, ∠Q = 90°, ∠R = 60° 2d) two, ∠K = 102.8°, ∠L = 39.9° or ∠K = 2.6°, ∠L = 140.1° 2e) no triangles are possible 2f) two, ∠A = 65.1°, ∠C = 66.9° or ∠A = 18.9°, ∠C = 113.1° 2g) one, ∠Y = 34.3°, ∠Z = 25.6° 2h) no triangles are possible 3a) ∠B = 34.4°, ∠C = 100.6°, c = 41.7 cm 3b) ∠P = 131.9°, ∠Q = 48.1°, p = 54.4 cm or ∠P = 7.8°, ∠Q = 131.9°, p = 7.4 cm

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