Question

solve for x. round to the nearest tenth, if necessary. triangle image with right angle at s, angle at t is 53 degrees, side ts is 2.7, side rs is x

Explanation:

Step1: Identify trigonometric ratio

We use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$. Here, $\theta=53^\circ$, opposite side is $x$, adjacent side is $2.7$.

Step2: Rearrange to solve for $x$

$x = 2.7 \times \tan(53^\circ)$

Step3: Calculate the value

Using $\tan(53^\circ)\approx1.3270$, we get $x\approx2.7\times1.3270$
$x\approx3.5829$

Step4: Round to nearest tenth

Round $3.5829$ to one decimal place.

Answer:

$3.6$