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: Identify the trigonometric ratio

We know the opposite side ($22$) and the adjacent side ($32$) to the angle $x$. We use the tangent ratio $\tan x=\frac{\text{opposite}}{\text{adjacent}}$. So, $\tan x=\frac{22}{32}=\frac{11}{16}$.

Step2: Find the angle

We need to find $x$, and since $\tan x=\frac{11}{16}$, then $x = \arctan(\frac{11}{16})$. Using a calculator, $x=\arctan(\frac{11}{16})\approx34.5^{\circ}$. Rounding to the nearest degree, $x = 34^{\circ}$.

Answer:

$34$