Question

Help please! show work thanks

Answer 1

answers
b = 2.77 m
A = 43.0°
C = 111.1°

cosine law to find b


`b^2 = a^2 + c^2 -2ac \cos B \\ \\ b = √(a^2 + c^2 -2ac \cos B) \\ \\ b = √(4.33^2 + 5.92^2 - 2(4.33)(5.92) \cos 25.9) \\ b = 2.7708\ m`

b = 2.7708\ m

Find angle A with sine law


`\displaystyle (\sin A)/(a) = (\sin B)/(b) \\ \\ \sin A = (a \sin B)/(b) \\ \\ A = \sin^(-1) \left[ (a \sin B)/(b) \right] \\ \\ A = \sin^(-1) \left[ (4.33 \sin 25.9)/(2.7708) \right] \\ \\ A = 43.0467020`

Find C with angles in triangle sum to 180

A + B + C = 180
C = 180 - A - B
C = 180 - 43.0467020 - 25.9
C = 111.1