Given in triangle ABC , m∠A = 75°, m∠B = 65°, a = 23.5ft.
We have to find the third angle,
[tex]m\angle C=180-75-65=40[/tex]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:
[tex]\begin{gathered} \frac{\sin A}{a}=\frac{\sin C}{c} \\ \Rightarrow\frac{\sin75}{23.5}=\frac{\sin 40}{c} \\ \Rightarrow\frac{0.966}{23.5}=\frac{0.643}{c} \\ \Rightarrow0.0411=\frac{0.643}{c} \\ \Rightarrow c=\frac{0.643}{0.0411} \\ \Rightarrow c=15.6 \end{gathered}[/tex]Thus. the length of the shortest side is 15.6 ft.