Question

current attempt in progress
please view the following video before answering this question. lecture video, section 4.4, example 02
note: the figure is not drawn to scale.
solve the triangle.
round the answers to the nearest integer.
γ =

b =

a =

Explanation:

Step1: Find angle \(\gamma\)

The sum of angles in a triangle is \(180^{\circ}\). So \(\gamma=180^{\circ}-45^{\circ}-51^{\circ}\)
\(\gamma = 84^{\circ}\)

Step2: Use the Law of Sines to find \(a\)

The Law of Sines states \(\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}\). Here \(A = 45^{\circ}\), \(C=84^{\circ}\), \(c = 30\) ft. So \(\frac{a}{\sin45^{\circ}}=\frac{30}{\sin84^{\circ}}\)
\(a=\frac{30\times\sin45^{\circ}}{\sin84^{\circ}}\)
\(\sin45^{\circ}=\frac{\sqrt{2}}{2}\approx0.707\), \(\sin84^{\circ}\approx0.994\)
\(a=\frac{30\times0.707}{0.994}\approx21\) ft

Step3: Use the Law of Sines to find \(b\)

Using \(\frac{b}{\sin51^{\circ}}=\frac{30}{\sin84^{\circ}}\)
\(\sin51^{\circ}\approx0.777\)
\(b=\frac{30\times\sin51^{\circ}}{\sin84^{\circ}}=\frac{30\times0.777}{0.994}\approx23\) ft

Answer:

\(\gamma = 84\)
\(b = 23\)
\(a = 21\)