Question

given the triangle
21
27° 30°
x
, 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 states that \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Let \(a = 21\), \(A = 27^{\circ}\), \(B=30^{\circ}\), and \(b=x\). So, \(\frac{21}{\sin27^{\circ}}=\frac{x}{\sin30^{\circ}}\).

Step2: Solve for \(x\)

Cross - multiply to get \(x=\frac{21\times\sin30^{\circ}}{\sin27^{\circ}}\).
We know that \(\sin30^{\circ}=\frac{1}{2}=0.5\) and \(\sin27^{\circ}\approx0.4540\).
Then \(x=\frac{21\times0.5}{0.4540}=\frac{10.5}{0.4540}\approx23.1277\).

Answer:

\(23.1277\)