Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
fill in the missing information.
text should be lower case.
sinx =
calculate the value for x.
answer (round to nearest degree): x =

Explanation:

Step1: Recall the sine formula

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For angle $x$, the opposite side is $33$ and the hypotenuse is $45$. So, $\sin x=\frac{33}{45}$.

Step2: Simplify the fraction

$\frac{33}{45}=\frac{11}{15}\approx0.7333$.

Step3: Find the angle using the inverse sine function

We know that $x = \sin^{-1}(\sin x)$. So, $x=\sin^{-1}(0.7333)$. Using a calculator, $\sin^{-1}(0.7333)\approx47^{\circ}$.

Answer:

For $\sin x=\frac{33}{45}$; $x = 47^{\circ}$