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 \(a = 12\), \(A=33^{\circ}\), \(B = 21^{\circ}\), and \(b=x\). Then \(\frac{12}{\sin33^{\circ}}=\frac{x}{\sin21^{\circ}}\).

Step2: Solve for \(x\)

Cross - multiply the equation \(\frac{12}{\sin33^{\circ}}=\frac{x}{\sin21^{\circ}}\) to get \(x=\frac{12\times\sin21^{\circ}}{\sin33^{\circ}}\).
We know that \(\sin21^{\circ}\approx0.3584\) and \(\sin33^{\circ}\approx0.5446\).
Substitute the values: \(x=\frac{12\times0.3584}{0.5446}\).
First, calculate \(12\times0.3584 = 4.3008\).
Then, \(x=\frac{4.3008}{0.5446}\approx7.8972\).

Answer:

\(7.8972\)