Question

find the perimeter of △qrs. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

Explanation:

Step1: Find the third - angle of $\triangle QRS$

The sum of angles in a triangle is $180^{\circ}$. Let the third - angle be $\angle S$. So, $\angle S=180-(68 + 26)=86^{\circ}$.

Step2: Use the Law of Sines to find side $x$

The Law of Sines states that $\frac{a}{\sin A}=\frac{b}{\sin B}=\frac{c}{\sin C}$. For $\triangle QRS$, we have $\frac{x}{\sin68^{\circ}}=\frac{40}{\sin86^{\circ}}$. Then $x = \frac{40\sin68^{\circ}}{\sin86^{\circ}}$.
$\sin68^{\circ}\approx0.9272$, $\sin86^{\circ}\approx0.9976$. So $x=\frac{40\times0.9272}{0.9976}\approx37.2$.

Step3: Calculate the perimeter of $\triangle QRS$

The perimeter $P$ of $\triangle QRS$ is $P = 40+60 + x$. Substitute $x\approx37.2$ into the formula. Then $P=40 + 60+37.2=137.2$.

Answer:

$137.2$