The board, fence and ground form a right special triangle. The angles are 30, 60 and 90. Since the board is 4 feet, it forms the hypotenuse of the triangle. The side opposite the 30 degrees (fence side) is 2 feet, or half of the hypotenuse. The side opposite the 60 degrees (ground side) is 2 times square root 3, which is approximately 3.464 feet.

The inscribed circle, or incircle, of the triangle is the largest diameter pipe that will fit. The equation for the radius of the circle is 2 times the area of the triangle divided by the perimeter of the triangle (2a/p).

In this problem, the area of the triangle is .5bh = .5(2)(2sqrt(3)) = 2sqrt(3).

The perimeter is 2+2sqrt(3)+4 = 6+2sqrt(3)

radius = 2(2sqrt(3))/(6+2sqrt(3)) = 6.928/9.464 = .732

The radius of the pipe is approximately .732 feet.

The diameter of the larget pipe is 2(.732) = **1.464 feet.**

## We’ll help your grades soar

Start your 48-hour free trial and unlock all the summaries, Q&A, and analyses you need to get better grades now.

- 30,000+ book summaries
- 20% study tools discount
- Ad-free content
- PDF downloads
- 300,000+ answers
- 5-star customer support

Already a member? Log in here.

Are you a teacher? Sign up now