Question

solve for x. round to the nearest tenth of a degree, if ne
(image of a right triangle with right angle at h, side hg = 44, hypotenuse ig = 65, angle at i is x degrees)
answer attempt 1 out of 2

Explanation:

Step1: Identify the trigonometric ratio

In right - triangle \( \triangle HIG\) with \( \angle H = 90^{\circ}\), we know the hypotenuse \( IG = 65\) and the side opposite to \(x\) is \( HG=44\). We use the sine ratio \( \sin x=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \( \sin x=\frac{44}{65}\).

Step2: Solve for \(x\)

Take the inverse - sine of both sides. \(x = \sin^{- 1}(\frac{44}{65})\). Using a calculator, \(x=\sin^{-1}(0.676923)\).

Answer:

\(x\approx42.6^{\circ}\)