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 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

We know that \(a = 18\), \(A=55^{\circ}\), and \(B = 44^{\circ}\). Substituting these into \(\frac{a}{\sin A}=\frac{b}{\sin B}\), we get \(b=\frac{a\sin B}{\sin A}\).

Step3: Calculate the sine values

We know that \(\sin55^{\circ}\approx0.8192\) and \(\sin44^{\circ}\approx0.6947\).

Step4: Compute the value of \(b\)

Substitute the sine values and \(a = 18\) into \(b=\frac{a\sin B}{\sin A}\):

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Answer:

15.3