Question

find v.
triangle with 30°, 60°, right angle, side 9√6 km, side v
write your answer in simplest radical form.
blank kilometers

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 \(9\sqrt{6}\) km and the hypotenuse is \(v\). So, \(\cos30^{\circ}=\frac{9\sqrt{6}}{v}\).

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

Since \(\cos30^{\circ}=\frac{\sqrt{3}}{2}\), we have \(\frac{\sqrt{3}}{2}=\frac{9\sqrt{6}}{v}\).

Step3: Solve for \(v\)

Cross - multiply: \(v\times\sqrt{3}=2\times9\sqrt{6}\). Then \(v=\frac{18\sqrt{6}}{\sqrt{3}}\). Rationalize the denominator: \(v = 18\sqrt{\frac{6}{3}}=18\sqrt{2}\).

Answer:

\(18\sqrt{2}\)