Question

what is the value of y in the triangle? a. 3 b. 6 c. 6√3 d. 3√3

Explanation:

Step1: Use cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 30^{\circ}\), adjacent side \(y\), hypotenuse \(6\sqrt{3}\). But we can also use the property of \(30 - 60-90\) triangle. In a \(30 - 60 - 90\) triangle, if the side opposite to \(30^{\circ}\) is \(a\), the side opposite to \(60^{\circ}\) is \(a\sqrt{3}\) and the hypotenuse is \(2a\).
Another way: Using \(\cos30^{\circ}=\frac{y}{6}\). Since \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\), we have \(y = 6\times\frac{\sqrt{3}}{2}=3\sqrt{3}\)

Answer:

D. \(3\sqrt{3}\)