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.
cosx =
calculate the value for x.
answer (round to nearest degree): x =

Explanation:

Step1: Recall cosine definition

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. For angle $X$, the adjacent side to angle $X$ is $17$ and the hypotenuse is $21$. So, $\cos X=\frac{17}{21}$.

Step2: Find the angle $X$

We know that if $\cos X=\frac{17}{21}$, then $X = \cos^{-1}(\frac{17}{21})$. Using a calculator, $X=\cos^{-1}(\frac{17}{21})\approx35.69^{\circ}$. Rounding to the nearest degree, $X\approx36^{\circ}$.

Answer:

$\cos X=\frac{17}{21}$, $X = 36$