Question

Arielle is building the wooden framework for the roof of a house. She needs the angle created by the vertical and horizontal boards of the frame to be a right angle. The height of the vertical board is 12 feet. The length of the horizontal board is 15 feet. The support beam that will connect the ends of the two boards measures 20 feet.

Which is true regarding the triangular frame?

It is an acute triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.
It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board to create a right triangle.
It is an acute triangle. About 7 feet need to be removed from the 20-foot board to create a right triangle.
It is an obtuse triangle. About 7 feet need to be removed from the 20-foot board to create a right triangle.

Answer 1

Compare 20^2 with 12^2 + 15^2: 20^2 = 400 while 12^2 + 15^2 = 144 + 225 = 369. Since 400 > 369, the angle opposite the 20-ft side is obtuse. A right triangle would require the support to be sqrt(369) ≈ 19.209 ft, so about 20 − 19.209 ≈ 0.79 ft (≈ 9.5 in) must be removed.

Answer: It is an obtuse triangle. About 0.8 foot needs to be removed from the 20-foot board.