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