Question

for the right triangle below, find the length of x. 10 x <-- 55a x = question help: video

Explanation:

Step1: Identify trigonometric ratio

We know the adjacent - side to the given angle and want to find the opposite - side. We use the tangent function. $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$.

Step2: Substitute values

Given $\theta = 55^{\circ}$ and the adjacent side $a = 10$. So $\tan(55^{\circ})=\frac{x}{10}$.

Step3: Solve for x

$x = 10\times\tan(55^{\circ})$. Since $\tan(55^{\circ})\approx1.4281$, then $x\approx10\times1.4281 = 14.281$.

Answer:

$14.281$