Question

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

Explanation:

Step1: Use cosine formula

In a right - angled triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here \(\theta = 30^{\circ}\), adjacent side \(y\) and hypotenuse \(6\). So \(\cos30^{\circ}=\frac{y}{6}\).

Step2: Substitute the value of \(\cos30^{\circ}\)

Since \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\), we have \(\frac{\sqrt{3}}{2}=\frac{y}{6}\).

Step3: Solve for \(y\)

Cross - multiply: \(y = 6\times\frac{\sqrt{3}}{2}=3\sqrt{3}\).

Answer:

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