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: Recall the sine formula

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. Here, the side opposite to the angle $x$ is $18$ and the hypotenuse is $20$. So, $\sin x=\frac{18}{20}=0.9$.

Step2: Find the angle using inverse sine

We know that if $\sin x = a$, then $x=\sin^{- 1}(a)$. So, $x=\sin^{-1}(0.9)$. Using a calculator, $\sin^{-1}(0.9)\approx64.16^{\circ}$.

Step3: Round to the nearest degree

Rounding $64.16^{\circ}$ to the nearest degree gives $64^{\circ}$.

Answer:

$64^{\circ}$