Question

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

answer attempt 1 out of 2

Explanation:

Step1: Identify the trigonometric ratio

In a right - triangle \( \triangle MNO\) with right - angle at \(N\), we know the opposite side (\(ON = 1.8\)) and the adjacent side (\(MN=1\)) with respect to the angle \(x\). The tangent ratio is given by \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). So, \(\tan x=\frac{ON}{MN}\).

Step2: Substitute the values

Substitute \(ON = 1.8\) and \(MN = 1\) into the tangent formula. We get \(\tan x=\frac{1.8}{1}=1.8\).

Step3: Solve for \(x\)

To find \(x\), we use the inverse tangent function. \(x=\tan^{- 1}(1.8)\). Using a calculator, \(x\approx60.9^{\circ}\).

Answer:

\(60.9^{\circ}\)