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 \(6.1\) and the side adjacent to angle \(x\) is \(3.2\). So, \(\tan x=\frac{6.1}{3.2}\).

Step2: Solve for \(x\)

Take the inverse tangent (arctan) of both sides. \(x = \arctan(\frac{6.1}{3.2})\).
Using a calculator, \(\frac{6.1}{3.2}=1.90625\), and \(x=\arctan(1.90625)\approx62.3^{\circ}\)

Answer:

\(x\approx62.3^{\circ}\)