Question

given the triangle
, find the length of side ( x ) using the law of sines. round your final answer to 4 decimal places.
( x = )
question help: video

Explanation:

Step1: Recall the Law of Sines formula

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Let \(a = 18\), \(A=58^{\circ}\), \(B = 27^{\circ}\), and \(b=x\). Then \(\frac{18}{\sin58^{\circ}}=\frac{x}{\sin27^{\circ}}\).

Step2: Solve for \(x\)

Cross - multiply to get \(x=\frac{18\times\sin27^{\circ}}{\sin58^{\circ}}\).
We know that \(\sin27^{\circ}\approx0.4540\) and \(\sin58^{\circ}\approx0.8480\).
Substitute the values: \(x=\frac{18\times0.4540}{0.8480}\).
First, calculate \(18\times0.4540 = 8.172\).
Then, \(x=\frac{8.172}{0.8480}\approx9.6368\).

Answer:

\(9.6368\)