Question

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

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle, the tangent of an angle \(x\) is given by \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the opposite side to angle \(x\) is \(ON = 1.8\) and the adjacent side is \(MN=1\). So, \(\tan x=\frac{1.8}{1}\).

Step2: Solve for \(x\)

We know that if \(\tan x = a\), then \(x=\tan^{- 1}(a)\). Since \(a = 1.8\), we have \(x=\tan^{-1}(1.8)\). Using a calculator, \(x\approx60.9^{\circ}\).

Answer:

\(x\approx60.9^{\circ}\)