Question

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

Explanation:

Step1: Apply the Law of Sines formula

The Law of Sines formula is \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Let \(a = 15\), \(A=27^{\circ}\), \(B = 18^{\circ}\), and \(b=x\).

Step2: Substitute values into the formula

Substituting the values into \(\frac{15}{\sin27^{\circ}}=\frac{x}{\sin18^{\circ}}\).

Step3: Solve for \(x\)

Cross - multiply to get \(x=\frac{15\times\sin18^{\circ}}{\sin27^{\circ}}\).
We know that \(\sin18^{\circ}\approx0.3090\) and \(\sin27^{\circ}\approx0.4540\).
Then \(x=\frac{15\times0.3090}{0.4540}=\frac{4.635}{0.4540}\approx10.2092\).

Answer:

\(10.2092\)