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 side opposite to angle \(x\) is \(FG = 7.8\) and the side adjacent to angle \(x\) is \(GH=6\). So, \(\tan x=\frac{7.8}{6}\).

Step2: Calculate \(\frac{7.8}{6}\)

\(\frac{7.8}{6}=1.3\). Then, \(x = \tan^{- 1}(1.3)\).

Step3: Find the value of \(x\)

Using a calculator, \(x=\tan^{-1}(1.3)\approx52.4^{\circ}\)

Answer:

\(52.4^{\circ}\)