Question

find d.
30°
60°
3 yd
write your answer in simplest radical form.
yards

Explanation:

Step1: Use the cosine function

In a right - triangle, \(\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}\). Here, \(\theta = 30^{\circ}\), the adjacent side is \(3\) yd and the hypotenuse is \(d\). So, \(\cos30^{\circ}=\frac{3}{d}\).

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

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

Step3: Solve for \(d\)

Cross - multiply: \(d\times\sqrt{3}=3\times2\). Then \(d=\frac{6}{\sqrt{3}}\). Rationalize the denominator: \(d = \frac{6\sqrt{3}}{\sqrt{3}\times\sqrt{3}}=\frac{6\sqrt{3}}{3}=2\sqrt{3}\).

Answer:

\(2\sqrt{3}\) yards