Question

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

Explanation:

Step1: Identify trigonometric ratio

In right triangle $ABC$, for $\angle C=70^\circ$, side $BC=x$ is adjacent, side $AB=8$ is opposite. Use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(70^\circ)=\frac{8}{x}$

Step2: Rearrange to solve for $x$

Isolate $x$ by cross-multiplying: $x=\frac{8}{\tan(70^\circ)}$

Step3: Calculate the value

Use $\tan(70^\circ)\approx2.747$:
$x\approx\frac{8}{2.747}\approx2.9$

Answer:

2.9