Question

find the length of the indicated side. 1 point 20.8 11.7 21.4 50.8 what is the length of the long leg of a 30 - 60 - 90?

Explanation:

Step1: Use trigonometric ratio

In a right - triangle, \(\tan\theta=\frac{\text{opposite}}{\text{adjacent}}\). Here, \(\theta = 57^{\circ}\), the opposite side is \(33\) and the adjacent side is \(x\). So, \(\tan57^{\circ}=\frac{33}{x}\).

Step2: Solve for \(x\)

We know that \(\tan57^{\circ}\approx1.54\). Then \(x=\frac{33}{\tan57^{\circ}}\). Substitute \(\tan57^{\circ}\approx1.54\) into the formula: \(x=\frac{33}{1.54}\approx21.4\).

Answer:

\(21.4\)