Question

solve for ( x ). round to the nearest tenth, if necessary.
right triangle with right angle at t, hypotenuse su = 9.9, angle at s is ( 19^circ ), and leg st = ( x )

Explanation:

Step1: Identify trigonometric ratio

In right triangle STU, angle at S is $19^\circ$, side opposite to $\angle S$ is $UT$, side adjacent is $x$, hypotenuse is $SU=9.9$. We use tangent: $\tan(\theta)=\frac{\text{opposite}}{\text{adjacent}}$
$\tan(19^\circ)=\frac{x}{9.9}$

Step2: Isolate x to solve

Rearrange to solve for x:
$x = 9.9 \times \tan(19^\circ)$
Calculate $\tan(19^\circ)\approx0.3443$, so:
$x \approx 9.9 \times 0.3443$

Step3: Compute final value

$x \approx 3.40857$
Round to nearest tenth: $x\approx3.4$

Answer:

$3.4$