Question

unit review - right triangles and trigonometry
solve for b.
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 \(C\).
\(C = 180^{\circ}-82^{\circ}-55^{\circ}=43^{\circ}\)

Step2: Apply the Law of Sines

According to the Law of Sines \(\frac{a}{\sin A}=\frac{b}{\sin B}\). Here \(a = 8\), \(A = 43^{\circ}\), \(B = 55^{\circ}\)
\(\frac{8}{\sin43^{\circ}}=\frac{b}{\sin55^{\circ}}\)
Cross - multiply: \(b=\frac{8\times\sin55^{\circ}}{\sin43^{\circ}}\)
We know that \(\sin43^{\circ}\approx0.682\), \(\sin55^{\circ}\approx0.819\)
\(b=\frac{8\times0.819}{0.682}=\frac{6.552}{0.682}\approx9.6\)

Answer:

\(9.6\)