Question

what is the value of y
18
30°
√3
9
9√3
18

Explanation:

Step1: Recall the cosine formula

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the hypotenuse \(c = 18\), and the adjacent side to the \(30^{\circ}\) angle is \(y\).

Step2: Substitute the values into the cosine formula

We know that \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\). Using the formula \(\cos\theta=\frac{y}{18}\) (since \(\theta = 30^{\circ}\), adjacent \(=y\), hypotenuse \(=18\)), we get \(y = 18\times\cos30^{\circ}\).

Step3: Calculate the value of \(y\)

Substitute \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\) into the equation \(y = 18\times\cos30^{\circ}\). Then \(y=18\times\frac{\sqrt{3}}{2}\). Simplify \(18\times\frac{\sqrt{3}}{2}\): \(18\div2 = 9\), so \(y = 9\sqrt{3}\).

Answer:

\(9\sqrt{3}\)