Question

trig ratios practice due: october 8 at 8:00 am grade: 50% question solve for x. round to the nearest tenth, if necessary. 1. identifying trig ratios (diagram), level 3. identifying trig ratios (diagram), level using trig to find a side trig word problems (diagram given) level 1 scientific calculator graphing calculator answer attempt 1 out of 2

Explanation:

Step1: Identify the trig - ratio

We know that in a right - triangle, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta = 65^{\circ}$, the opposite side to the angle $\theta$ is $x$ and the adjacent side is $80$. So we use the tangent function: $\tan(65^{\circ})=\frac{x}{80}$.

Step2: Solve for $x$

Multiply both sides of the equation $\tan(65^{\circ})=\frac{x}{80}$ by $80$ to isolate $x$. We get $x = 80\times\tan(65^{\circ})$.
Since $\tan(65^{\circ})\approx2.1445$, then $x=80\times2.1445 = 171.56$.
Rounding to the nearest tenth, $x\approx171.6$.

Answer:

$171.6$