Question

1. find the missing variables.

34
x=
y=

Explanation:

Step1: Use cosine for \(x\)

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 30^{\circ}\), adjacent side is \(x\), hypotenuse is \(34\).
\(\cos30^{\circ}=\frac{x}{34}\)
Since \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\), we have \(x = 34\times\frac{\sqrt{3}}{2}=17\sqrt{3}\approx29.44\)

Step2: Use sine for \(y\)

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here \(\theta = 30^{\circ}\), opposite side is \(y\), hypotenuse is \(34\).
\(\sin30^{\circ}=\frac{y}{34}\)
Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(y = 34\times\frac{1}{2}=17\)

Answer:

\(x = 17\sqrt{3}\approx29.44\), \(y = 17\)