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 \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). In this triangle, let \(a = 20\), \(A=43^{\circ}\), \(B = 19^{\circ}\), and \(b=x\). So, \(\frac{20}{\sin43^{\circ}}=\frac{x}{\sin19^{\circ}}\).

Step2: Solve for \(x\)

Cross - multiply the equation from Step1: \(x=\frac{20\times\sin19^{\circ}}{\sin43^{\circ}}\).
We know that \(\sin19^{\circ}\approx0.3256\) and \(\sin43^{\circ}\approx0.6820\).
Then \(x=\frac{20\times0.3256}{0.6820}\).
First, calculate \(20\times0.3256 = 6.512\).
Then \(x=\frac{6.512}{0.6820}\approx9.5484\).

Answer:

\(9.5484\)