Question

determine the remaining sides and angles of the triangle abc.
a = 85° (round to the nearest degree as needed.)
b ≈ □ m
(do not round until the final answer. then 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 \(a = 10\) m, \(A=85^{\circ}\), \(B = 61^{\circ}\), \(C=34^{\circ}\). To find \(b\), we use \(\frac{a}{\sin A}=\frac{b}{\sin B}\).

Step2: Solve for \(b\)

Rearrange the formula to \(b=\frac{a\sin B}{\sin A}\). Substitute \(a = 10\), \(\sin B=\sin61^{\circ}\approx0.8746\), \(\sin A=\sin85^{\circ}\approx0.9962\).

$$ b=\frac{10\times0.8746}{0.9962} $$

$$ b=\frac{8.746}{0.9962}\approx8.78 $$

Answer:

\(b\approx8.78\) m