Question

1. x 55° 8

Explanation:

Step1: Use tangent function

In a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here $\theta = 55^{\circ}$ and the adjacent side to the $55^{\circ}$ angle is 8, and the opposite side is $x$. So $\tan(55^{\circ})=\frac{x}{8}$.

Step2: Solve for $x$

We know that $\tan(55^{\circ})\approx1.4281$. Then $x = 8\times\tan(55^{\circ})$. So $x\approx8\times1.4281 = 11.4248\approx11.42$.

Answer:

$x\approx11.42$