Question

An architect is designing a circular window to be installed in the

gable of a house. The metal window frame will be 1 foot wide and will be bordered by
the roof above and a wood beam below. The distance from the center of the window to the roof is 3 feet. What will be the circumference of the circular glass pane that will be
needed?

Answer 1

12.57 ft

Explanation:

First thing we need to find is the radius of the circular glass pane. We are given the information that the center of the glass plane is directly in the center of the triangle and that the closest distance from the center to the roof is 3 ft, including a metal border with a width of 1 ft.

Since the metal frame is the same width all the way around the window, we can safely conclude that the radius of the circular glass pane is 2 ft, as the 3ft measurement included the radius and the metal frame.

Now that we have our radius we can use the formula:

`C=2\pi r` (Circumference = 2 x pi x radius)

Using 3.14 for pi we get:

`C=2(3.14)(2)`

`C=4 \pi` or 12.57 ft (2.d.p)