Question

Use what you know about the relationships in 456$30-60-90$ right triangles to solve the following problem. A stained-glass window is in the shape of an equilateral triangle with sides that are 789$36$ inc10hes long. How long is the perpendicular11 bisector of any si12de?Answers:$18\sqrt{3}$ inches$18$ inches$9$ inches$36$ inches

Answer 1

In an equilateral triangle, the perpendicular bisector from a vertex to the opposite side is the altitude. Splitting the triangle gives a 30-60-90 right triangle with hypotenuse 36 and short leg 18 (half the base). The longer leg (altitude) is 18√3.

Answer: 18√3 inches.