Question

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

Explanation:

Step1: Identify triangle type and trigonometric ratio

This is a right - triangle (right - angled at \(H\)). We know the opposite side (\(HG = 44\)) and the hypotenuse (\(IG=65\)) with respect to angle \(x\) (at \(I\)). The sine of an angle in a right - triangle is defined as \(\sin(x)=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(x)=\frac{HG}{IG}=\frac{44}{65}\).

Step2: Calculate the value of \(x\)

We need to find \(x\) such that \(\sin(x)=\frac{44}{65}\). First, calculate \(\frac{44}{65}\approx0.6769\). Then, take the inverse sine (arcsin) of \(0.6769\) to find \(x\). Using a calculator, \(x=\arcsin(0.6769)\).

Step3: Round to the nearest tenth of a degree

Using a calculator, \(\arcsin(0.6769)\approx42.6^{\circ}\) (rounded to the nearest tenth of a degree).

Answer:

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