Question

1. 19 23 x°

Explanation:

Step1: Use trigonometric ratio (tangent)

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, if \(\theta = x^{\circ}\), the opposite side is \(19\) and the adjacent side is \(23\). So, \(\tan x=\frac{19}{23}\).

Step2: Find the angle using inverse tangent

\(x = \tan^{- 1}(\frac{19}{23})\). Using a calculator, \(\frac{19}{23}\approx0.826\), and \(\tan^{-1}(0.826)\approx39.4^{\circ}\)

Answer:

\(x\approx39.4^{\circ}\)