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 = \frac{}{}
calculate the value for x.
answer (round to nearest degree): x = square

Explanation:

Step1: Recall sine definition

The sine of an angle in a right - triangle is defined as $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$. For angle $X$, the opposite side is 33 and the hypotenuse is 45. So, $\sin X=\frac{33}{45}$.

Step2: Calculate the angle

We know that if $\sin X=\frac{33}{45}$, then $X = \sin^{-1}(\frac{33}{45})$. First, $\frac{33}{45}\approx0.7333$. Then $X=\sin^{-1}(0.7333)$. Using a calculator, $X\approx47.13^{\circ}$. Rounding to the nearest degree, $X = 47^{\circ}$.

Answer:

$\sin X=\frac{33}{45}$
$X = 47$