Question

find the length of side a.
c = 21.8° a = 98.2° a =?
round to the nearest tenth.

Explanation:

Step1: Apply the Law of Sines

The Law of Sines states that \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). In this triangle, \(b = 3\), \(B=60^{\circ}\), and \(A = 98.2^{\circ}\). We want to find \(a\). Using the formula \(\frac{a}{\sin A}=\frac{b}{\sin B}\), we can rewrite it as \(a=\frac{b\times\sin A}{\sin B}\).

Step2: Substitute the values

Substitute \(b = 3\), \(A = 98.2^{\circ}\), and \(B = 60^{\circ}\) into the formula. \(\sin A=\sin(98.2^{\circ})\approx0.990\), \(\sin B=\sin(60^{\circ})=\frac{\sqrt{3}}{2}\approx0.866\). Then \(a=\frac{3\times0.990}{0.866}\).

Step3: Calculate the value

\(a=\frac{2.97}{0.866}\approx3.4\).

Answer:

\(3.4\)