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

In a right - triangle, for an acute angle \(x\), \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to angle \(x\) is \(22\) and the adjacent side is \(32\). So, \(\tan x=\frac{22}{32}\).

Step2: Simplify the ratio

\(\frac{22}{32}=\frac{11}{16}\approx0.6875\).

Step3: Find the angle \(x\)

We know that \(x = \tan^{- 1}(0.6875)\). Using a calculator, \(x=\tan^{-1}(0.6875)\approx34^{\circ}\) (rounded to the nearest degree).

Answer:

\(34\)