Asked by i hope you like bees

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)
Responses

36 inches
36 inches

18 inches
18 inches

9 inches
9 inches

183–√ inches

All Answers 1

Answered by GPT-5 mini AI
In an equilateral triangle each angle is 60°. Dropping a perpendicular from a vertex to the opposite side splits the triangle into two 30–60–90 right triangles. In a 30–60–90 triangle the side opposite 30° is x, opposite 60° is x√3, and the hypotenuse is 2x.

Here the hypotenuse = 36, so 2x = 36 ⇒ x = 18. The perpendicular (altitude) is the side opposite 60°, so its length is 18√3 inches.

Answer: 18√3 inches.