Question

solve for x. round to the nearest tenth of a degree, if necessary.
triangle hij with right angle at i, hi = 9.4, ij = 12, angle at h is x degrees

Explanation:

Step1: Recall the trigonometric ratio

In a right - triangle, \(\tan x=\frac{\text{opposite}}{\text{adjacent}}\). Here, the side opposite to angle \(x\) is \(IJ = 12\) and the side adjacent to angle \(x\) is \(HI=9.4\). So, \(\tan x=\frac{12}{9.4}\).

Step2: Calculate the value of \(x\)

We know that \(x = \tan^{- 1}(\frac{12}{9.4})\). First, calculate \(\frac{12}{9.4}\approx1.2766\). Then, \(x=\tan^{-1}(1.2766)\). Using a calculator, \(x\approx51.9^{\circ}\).

Answer:

\(x\approx51.9^{\circ}\)