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 \(a = 26\), \(A=13^{\circ}\), \(B = 23^{\circ}\), and \(b=x\). Then \(\frac{26}{\sin13^{\circ}}=\frac{x}{\sin23^{\circ}}\).

Step2: Solve for \(x\)

Cross - multiply the equation from Step1: \(x=\frac{26\times\sin23^{\circ}}{\sin13^{\circ}}\).
We know that \(\sin13^{\circ}\approx0.2225\) and \(\sin23^{\circ}\approx0.3907\).
Substitute the values: \(x=\frac{26\times0.3907}{0.2225}\).
First, calculate \(26\times0.3907 = 10.1582\).
Then, \(x=\frac{10.1582}{0.2225}\approx45.6548\).

Answer:

\(45.6548\)