Question

solve for a.
a =
round your final answer to the nearest tenth.
law of sines: $\frac{a}{\sin a}=\frac{b}{\sin b}=\frac{c}{\sin c}$

Explanation:

Step1: Find the third angle

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle be \(C\). Then \(C = 180^{\circ}-50^{\circ}-64^{\circ}=66^{\circ}\).

Step2: Apply the Law of Sines

By the Law of Sines \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Here \(A = 50^{\circ}\), \(b = 17\), \(B=64^{\circ}\). So \(a=\frac{17\times\sin(50^{\circ})}{\sin(64^{\circ})}\).
We know that \(\sin(50^{\circ})\approx0.766\), \(\sin(64^{\circ})\approx0.899\).
Then \(a=\frac{17\times0.766}{0.899}=\frac{13.022}{0.899}\approx14.5\)

Answer:

\(14.5\)