Question

use what you know about the relationships in 30 - 60 - 90 right triangles to solve the following problem. a stained - glass window is in the shape of an equilateral triangle with sides that are 36 inches long. how long is the perpendicular bisector of any side? (1 point) 18√3 inches 18 inches 36 inches 9 inches

Explanation:

Step1: Analyze the 30 - 60 - 90 triangle formed

When we draw the perpendicular bisector of a side of an equilateral triangle, we get two 30 - 60 - 90 right triangles. The side of the equilateral triangle (\(36\) inches) is the hypotenuse of the 30 - 60 - 90 triangle. The shorter leg (opposite the \(30^{\circ}\) angle) is half of the side of the equilateral triangle. So, the shorter leg \(a=\frac{36}{2}=18\) inches.

Step2: Use the ratio for the longer leg

In a 30 - 60 - 90 triangle, the ratio of the sides is \(a:a\sqrt{3}:2a\) (shorter leg : longer leg : hypotenuse). The perpendicular bisector is the longer leg (\(b\)) of the 30 - 60 - 90 triangle. Since \(a = 18\) inches and \(b=a\sqrt{3}\), then \(b = 18\sqrt{3}\) inches.

Answer:

\(18\sqrt{3}\) inches (the first option)