Question

1. find x.

image of a right triangle with one angle 50 degrees, adjacent side 17, hypotenuse x, and four multiple-choice options: 19.4, 22.2, 28.6, 26.4

Explanation:

Step1: Identify trigonometric ratio

The triangle is right - angled, and we know the adjacent side to the \(50^{\circ}\) angle (\(17\)) and we need to find the hypotenuse (\(x\)). The cosine ratio is \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). So, \(\cos(50^{\circ})=\frac{17}{x}\).

Step2: Solve for \(x\)

Rearrange the formula to \(x = \frac{17}{\cos(50^{\circ})}\). We know that \(\cos(50^{\circ})\approx0.6428\). Then \(x=\frac{17}{0.6428}\approx26.4\).

Answer:

26.4