Question

use the law of sines to find the missing side of the triangle. find the measure of b, given ( mangle a = 55^{circ}, mangle b = 44^{circ} ), and ( a = 18 ). 21.8 21.2 15.3 10.2

Explanation:

Step1: Recall the Law of Sines formula

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). We are given \(a = 18\), \(m\angle A=55^{\circ}\), and \(m\angle B = 44^{\circ}\). We want to find \(b\), so we use the formula \(\frac{a}{\sin A}=\frac{b}{\sin B}\).

Step2: Substitute the given values into the formula

Substitute \(a = 18\), \(\sin A=\sin(55^{\circ})\approx0.8192\), and \(\sin B=\sin(44^{\circ})\approx0.6947\) into \(\frac{a}{\sin A}=\frac{b}{\sin B}\). We get \(b=\frac{a\sin B}{\sin A}\).

Step3: Calculate the value of \(b\)

\(b=\frac{18\times\sin(44^{\circ})}{\sin(55^{\circ})}=\frac{18\times0.6947}{0.8192}=\frac{12.5046}{0.8192}\approx15.3\)

Answer:

\(15.3\)