Question

Triangle ABC , m∠A = 75°, m∠B = 65°, a = 23.5ftFind the length of the shortest side.Round to one decimal.

Answer 1

Given in triangle ABC , m∠A = 75°, m∠B = 65°, a = 23.5ft.

We have to find the third angle,

`m\angle C=180-75-65=40`

The shortest angle is angle C. So, the shortest side will be opposite to angle C.

Use the sine rule, to find the third side as follows:

`\begin{gathered} (\sin A)/(a)=(\sin C)/(c) \\ \Rightarrow(\sin75)/(23.5)=(\sin 40)/(c) \\ \Rightarrow(0.966)/(23.5)=(0.643)/(c) \\ \Rightarrow0.0411=(0.643)/(c) \\ \Rightarrow c=(0.643)/(0.0411) \\ \Rightarrow c=15.6 \end{gathered}`

Thus. the length of the shortest side is 15.6 ft.