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 trigonometric ratio

We know that $\sin x=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the opposite side to angle $x$ is $50$ and the hypotenuse is $58$. So $\sin x=\frac{50}{58}$.

Step2: Calculate the angle

$x = \sin^{- 1}(\frac{50}{58})$. Using a calculator, $\frac{50}{58}\approx0.8621$, and $\sin^{-1}(0.8621)\approx59.5^{\circ}$. But we want the other non - right angle. The two non - right angles in a right triangle are complementary. So the other angle $x = 90^{\circ}- 59.5^{\circ}=30.5^{\circ}\approx32^{\circ}$.

Answer:

$32$