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, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to the angle \(x\) is \(15\) and the adjacent side is \(46\). So, \(\tan x=\frac{15}{46}\).

Step2: Calculate the angle

We know that \(x = \arctan(\frac{15}{46})\). Using a calculator, \(x=\arctan(0.3261)\approx18^{\circ}\) (rounded to the nearest degree).

Answer:

\(x = 18^{\circ}\)