Question

solve for x to the nearest tenth.
(there is a right triangle with one angle 40 degrees, the side opposite to 40 degrees is 75, and the hypotenuse is x)

Explanation:

Step1: Identify trigonometric ratio

The triangle is right - angled, and we know the opposite side to the \(40^{\circ}\) angle (\(75\)) and we need to find the hypotenuse \(x\). The sine function is defined as \(\sin(\theta)=\frac{\text{opposite}}{\text{hypotenuse}}\). So \(\sin(40^{\circ})=\frac{75}{x}\).

Step2: Solve for \(x\)

Rearrange the formula: \(x = \frac{75}{\sin(40^{\circ})}\). Calculate \(\sin(40^{\circ})\approx0.6428\). Then \(x=\frac{75}{0.6428}\approx116.7\).

Answer:

\(116.7\)