Question

solve for x. round to the nearest tenth, if necessary. triangle image with right angle at t, angle at s is 72 degrees, side ut is 9.4, side su is x

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$, where $\theta=72^\circ$, opposite side $=9.4$, hypotenuse $=x$.

Step2: Substitute values into formula

$\sin(72^\circ)=\frac{9.4}{x}$

Step3: Rearrange to solve for $x$

$x=\frac{9.4}{\sin(72^\circ)}$

Step4: Calculate the value

$\sin(72^\circ)\approx0.9511$, so $x\approx\frac{9.4}{0.9511}\approx9.9$

Answer:

$9.9$