Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the
angle measures of the two acute angles.
calculate the value for x.
answer (round to nearest degree): x =

Explanation:

Step1: Identify the trigonometric ratio

We know the opposite side ($50$) and the hypotenuse ($58$) of the right - triangle. So, we use the sine ratio. The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Let the angle be $x$. Then $\sin x=\frac{50}{58}$.

Step2: Calculate the angle

We have $\sin x=\frac{50}{58}\approx0.8621$. To find $x$, we take the inverse sine (arcsin) of $0.8621$. So, $x = \sin^{-1}(0.8621)$. Using a calculator, $x\approx59^{\circ}$.

Answer:

$59$