Question

solve for x. round to the nearest tenth of a degree, if necessary.

Explanation:

Step1: Use the tangent function

In a right - triangle, the tangent of an angle \(x\) is defined as \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to angle \(x\) is \(FG = 57\) and the adjacent side is \(EF=63\). So, \(\tan x=\frac{57}{63}\).

Step2: Simplify the fraction and find the arctangent

First, simplify \(\frac{57}{63}=\frac{19}{21}\approx0.9048\). Then, \(x = \arctan(0.9048)\). Using a calculator, \(x=\tan^{- 1}(0.9048)\).

Answer:

\(x\approx42.1^{\circ}\)