Question

select the correct answer.

what is the value of (y) in the triangle?

3
6
(6sqrt{3})
(3sqrt{3})

Explanation:

Identify the given values

We have a right triangle.
The hypotenuse is \(6\).
One angle is \(30^\circ\).
The opposite angle is \(60^\circ\).
The side adjacent to \(30^\circ\) is \(y\).

Apply trigonometric ratios

We use the cosine ratio.
The cosine of \(30^\circ\) is adjacent over hypotenuse.

$$ \cos(30^\circ) = \frac{y}{6} $$

Solve for y

We know \(\cos(30^\circ) = \frac{\sqrt{3}}{2}\).

$$ \frac{\sqrt{3}}{2} = \frac{y}{6} $$

Multiply both sides by \(6\).

$$ y = 6 \cdot \frac{\sqrt{3}}{2} = 3\sqrt{3} $$

Answer:

• 3
• 6
• 6\(\sqrt{3}\)
• 3\(\sqrt{3}\) (Correct answer)