Question

in the right triangle, one angle is 56°, one leg is 28, and the hypotenuse is labeled x. we need to find the value of x or solve related problems (specific question content may be to find x using trigonometric functions or angle sum properties, etc.).

Explanation:

Step1: Identify trigonometric ratio

We use sine: $\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}$, where $\theta=56^\circ$, opposite side $=28$, hypotenuse $=x$.

Step2: Rearrange to solve for x

$x=\frac{28}{\sin(56^\circ)}$

Step3: Calculate value

First, $\sin(56^\circ)\approx0.8290$, so $x\approx\frac{28}{0.8290}\approx33.78$

Answer:

$x\approx33.8$ (rounded to one decimal place)