Question

What is the perimeter p of triangle ABC to the nearest whole number?

Answer 1

Find the missing angle of the triangle

$\begin{gathered} A=180-40-49 \\ A=180-89 \\ A=91 \end{gathered}$

apply the law of sines in order to find the missing sides

$\begin{gathered} \frac{26}{\sin49}=\frac{c}{\sin 40} \\ b=26\cdot\frac{\sin40}{\sin49} \\ b\cong22.14 \end{gathered}$

$\begin{gathered} \frac{26}{\sin49}=\frac{a}{\sin 91} \\ a=26\cdot\frac{\sin 91}{\sin 49} \\ a\cong34.33 \end{gathered}$

add the three sides to find the perimeter

$\begin{gathered} P=26+34.33+22.14 \\ P=82.47\cong82 \end{gathered}$