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: Find the third angle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(C\). Then \(C = 180-(14 + 15)=151^{\circ}\).

Step2: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Here, let \(a = 21\), \(A=14^{\circ}\), \(B = 15^{\circ}\), and \(b=x\). So \(\frac{21}{\sin14^{\circ}}=\frac{x}{\sin15^{\circ}}\).

Step3: Solve for \(x\)

Cross - multiply: \(x=\frac{21\times\sin15^{\circ}}{\sin14^{\circ}}\).
We know that \(\sin14^{\circ}\approx0.2419\), \(\sin15^{\circ}\approx0.2588\).
Then \(x=\frac{21\times0.2588}{0.2419}=\frac{5.4348}{0.2419}\approx22.4671\).

Answer:

\(22.4671\)