Question

solve for x in the triangle. round your answer to the nearest tenth. triangle image with 56° angle, right angle, side 15, and hypotenuse x x =

Explanation:

Step1: Identify trigonometric ratio

The triangle is right - angled, with one angle \(56^{\circ}\), the opposite side to \(56^{\circ}\) is \(15\), and \(x\) is the hypotenuse. We use the sine ratio: \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So \(\sin(56^{\circ})=\frac{15}{x}\).

Step2: Solve for \(x\)

Rearrange the formula: \(x = \frac{15}{\sin(56^{\circ})}\). Calculate \(\sin(56^{\circ})\approx0.8290\). Then \(x=\frac{15}{0.8290}\approx18.1\).

Answer:

\(18.1\)