Question

find k.
triangle with 30°, 60°, right angle, side 3√3 m, side k
write your answer in simplest radical form.
box meters

Explanation:

Step1: Use sine function

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\). Here \(\theta = 30^{\circ}\), the hypotenuse \(c = 3\sqrt{3}\) and the side \(k\) is opposite to the \(30^{\circ}\) angle.
\(\sin30^{\circ}=\frac{k}{3\sqrt{3}}\)

Step2: Substitute the value of \(\sin30^{\circ}\)

Since \(\sin30^{\circ}=\frac{1}{2}\), we have \(\frac{1}{2}=\frac{k}{3\sqrt{3}}\)

Step3: Solve for \(k\)

Cross - multiply: \(k=\frac{3\sqrt{3}}{2}\)

Answer:

\(\frac{3\sqrt{3}}{2}\) meters