Question

right triangle trigonometry - sohcahtoa
right triangle trigonometry relates the sides of a right triangle to the angle measures of the two acute angles.
fill in the missing information.
text should be lower case.
calculate the value for x.
answer (round to nearest degree): x = □°

Explanation:

Step1: Use 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 \(28\) and the adjacent side is \(47\). So, \(\tan x=\frac{28}{47}\).

Step2: Find the angle \(x\)

By the definition of the inverse tangent function, \(x = \arctan(\frac{28}{47})\). Using a calculator, \(\arctan(\frac{28}{47})\approx31^{\circ}\) (rounded to the nearest degree).

Answer:

$$x=\arctan{\frac{28}{47}}$$
$$x\approx31^{\circ}$$