Question

9 5000 ft 26° x = ft

Explanation:

Step1: Identify the trigonometric ratio

We have a right - triangle where the side opposite the angle \(26^{\circ}\) is \(5000\) ft and the hypotenuse is \(x\). We use the sine ratio \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). So, \(\sin(26^{\circ})=\frac{5000}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to \(x = \frac{5000}{\sin(26^{\circ})}\). We know that \(\sin(26^{\circ})\approx0.4384\). Then \(x=\frac{5000}{0.4384}\approx11405\).

Answer:

\(11405\)