Using the law of cosines, the missing measures of the triangle are:
a = 5.6 m; B = 43.3°; C = 99.7°.
What is the Law of Cosines?
a² = c² + b² − 2bc × cos(A)
Given the following:
m∠A = 37°
b = 6 cm
c = 9 cm
Apply the law of cosines formula to find a:
a² = 9² + 6² − 2(6)(9) × cos(37)
a = √[9² + 6² − 2(6)(9) × cos(37)] ≈ 5.6 m
Find B:
b² = a² + c² − 2ac × cos(B)
6² = 5.6² + 9² − 2(5.6)(9) × cos(B)
36 = 112.36 - 100.8 × cos(B)
36 - 112.36 = - 100.8 × cos(B)
-76.36 = - 100.8 × cos(B)
-76.36/-100.8 = cos(B)
0.7278 = cos(B)
B = cos^(-1)(0.7278)
B = 43.3°
C = 180 - 37 - 43.3 [triangle sum theorem]
C = 99.7°
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