Question

question 10
0/1 pt 3 99 details
find the remaining sides of a 30° - 60° - 90° triangle if the longest side is 18. answer exactly.
shortest side:
middle side:
question help: video

Explanation:

Step1: Recall side - length ratios

In a 30° - 60° - 90° triangle, the ratio of the sides is \(1:\sqrt{3}:2\), where the side opposite the 30° angle is the shortest, the side opposite the 60° angle is the middle - length side, and the side opposite the 90° angle is the longest. Let the shortest side be \(x\), the middle - length side be \(y\), and the longest side (hypotenuse) be \(c\). Then \(c = 2x\) and \(y=\sqrt{3}x\).

Step2: Find the shortest side

Given \(c = 18\), and \(c = 2x\). We solve for \(x\) by setting \(2x=18\), so \(x=\frac{18}{2}=9\).

Step3: Find the middle - length side

Since \(x = 9\) and \(y=\sqrt{3}x\), then \(y = 9\sqrt{3}\).

Answer:

Shortest side: 9
Middle side: \(9\sqrt{3}\)