Question

3 multiple choice 1 point use the law of sines to find the missing side of the triangle. find the measure of b, given ( mangle a = 63^{circ}, mangle b = 43^{circ} ), and ( a = 18 ). 23.5 13.8 10.9 27.0

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 want to find \(b\), so we use the formula \(\frac{a}{\sin A}=\frac{b}{\sin B}\).

Step2: Substitute the given values

We know that \(a = 18\), \(A=63^{\circ}\), and \(B = 43^{\circ}\). Substituting into the formula \(\frac{a}{\sin A}=\frac{b}{\sin B}\), we get \(b=\frac{a\sin B}{\sin A}\).

Step3: Calculate \(\sin A\) and \(\sin B\)

\(\sin A=\sin63^{\circ}\approx0.891\), \(\sin B=\sin43^{\circ}\approx0.682\).

Step4: Compute \(b\)

\(b=\frac{18\times0.682}{0.891}=\frac{12.276}{0.891}\approx13.8\)

Answer:

13.8