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 ($12$) and the adjacent side ($48$) relative to the angle \(x\). The tangent ratio is \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan x = \frac{12}{48}\).

Step2: Simplify the ratio

Simplify \(\frac{12}{48}=\frac{1}{4}= 0.25\). So, \(\tan x=0.25\).

Step3: Find the angle

To find \(x\), we use the inverse - tangent function \(x = \tan^{-1}(0.25)\). Using a calculator, \(x\approx14^{\circ}\) (rounded to the nearest degree).

Answer:

$14$