Question

solve for x. round to the nearest tenth, if necessary.

Explanation:

Step1: Identify trigonometric ratio

Since we know the adjacent side to the angle and want to find the opposite side in a right - triangle, we use the tangent function. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 66^{\circ}$, the adjacent side $RS=x$ and the opposite side $QR = 80$. So, $\tan66^{\circ}=\frac{80}{x}$.

Step2: Solve for x

We know that $\tan66^{\circ}\approx2.246$. Then, $2.246=\frac{80}{x}$. Cross - multiply to get $2.246x = 80$. Divide both sides by 2.246: $x=\frac{80}{2.246}\approx35.6$.

Answer:

$x\approx35.6$