Question

determine the remaining sides and angles of the triangle abc.
a = 26.21° b = 27.94° c = 15.55 m
c = 125.85°
a ≈ 8.47 m
(round to the nearest hundredth as needed.)
b ≈ m
(round to the nearest hundredth as needed.)

Explanation:

Step1: Use the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). We know \(A = 26.21^{\circ}\), \(B=27.94^{\circ}\), \(C = 125.85^{\circ}\), and \(c = 15.55\) m. We want to find \(b\), so we use \(\frac{b}{\sin B}=\frac{c}{\sin C}\).

Step2: Solve for \(b\)

Rearrange the formula to \(b=\frac{c\sin B}{\sin C}\). Substitute the values: \(b=\frac{15.55\times\sin(27.94^{\circ})}{\sin(125.85^{\circ})}\).
First, calculate \(\sin(27.94^{\circ})\approx0.468\) and \(\sin(125.85^{\circ})\approx0.814\).
Then \(b=\frac{15.55\times0.468}{0.814}\).
\(15.55\times0.468 = 7.2774\).
\(b=\frac{7.2774}{0.814}\approx8.94\)

Answer:

\(b\approx8.94\) m