Question

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

Explanation:

Step1: Use the tangent function

In a right - triangle, \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to angle \(x\) is \(FG = 7.8\) and the adjacent side is \(GH=6\). So, \(\tan x=\frac{7.8}{6}\).

Step2: Calculate the value of \(\tan x\)

\(\frac{7.8}{6}=1.3\). So, \(\tan x = 1.3\).

Step3: Find the value of \(x\)

We know that \(x=\arctan(1.3)\). Using a calculator, \(x=\arctan(1.3)\approx52.4^{\circ}\)

Answer:

\(x\approx52.4^{\circ}\)