Question

kuta software - infinite geometry
solving right triangles
find the missing side. round to th
1)
19.4

Explanation:

Step1: Use trigonometric ratio (cosine)

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 72^{\circ}\), adjacent side \(a = 6\), and hypotenuse \(x\). So, \(\cos(72^{\circ})=\frac{6}{x}\).

Step2: Solve for \(x\)

We can rewrite the equation as \(x=\frac{6}{\cos(72^{\circ})}\). Since \(\cos(72^{\circ})\approx0.3090\), then \(x=\frac{6}{0.3090}\approx19.4\).

Answer:

\(x\approx19.4\)