Question

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Answer 1

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

cosine law to find b

$b^2 = a^2 + c^2 -2ac \cos B \\ \\ b = \sqrt{a^2 + c^2 -2ac \cos B} \\ \\ b = \sqrt{4.33^2 + 5.92^2 - 2(4.33)(5.92) \cos 25.9} \\ b = 2.7708\ m$

b = 2.7708\ m

Find angle A with sine law

$\displaystyle \frac{\sin A}{a} = \frac{\sin B}{b} \\ \\ \sin A = \frac{a \sin B}{b} \\ \\ A = \sin^{-1} \left[ \frac{a \sin B}{b} \right] \\ \\ A = \sin^{-1} \left[ \frac{4.33 \sin 25.9}{2.7708} \right] \\ \\ A = 43.0467020$

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