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 = \square

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$. Here, the adjacent side to the angle $x$ is $14$ and the hypotenuse is $40$. So, $\cos x=\frac{14}{40}$.

Step2: Calculate the value of $x$

First, simplify $\frac{14}{40}=\frac{7}{20}=0.35$. Then, use the inverse cosine function $x = \cos^{-1}(0.35)$. Using a calculator, $x\approx21^{\circ}$ (rounded to the nearest degree).

Answer:

$21$