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.

The correct answer is:

It is an obtuse triangle; about 0.8 foot needs to be removed from the 20 foot board to create a right triangle.

Explanation:

To check the sides of the triangle to see if it forms a right triangle, we use the Pythagorean theorem:

a²+b²=c², where a and b are the legs of the triangle and c is the hypotenuse. Using 12 and 15 for the legs, we have:

12²+15² = c²

144+225 = c²

369 = c²

√369 = √c²

19.2 = c

We need to remove 0.8 foot from the 20-foot board.

The other thing we need to know is what kind of triangle the frame will make. Consider the angle at the top of the right triangle formed by the 15 foot board and the 12 foot board. 15 is the horizontal length and 12 is the vertical length. 15 would be across from the angle at the top, and 12 would be adjacent to this angle. The ratio opposite/adjacent is the ratio for tangent:

tan x = (15/12)

To find the measure of x, our unknown angle, we take the inverse tangent:

tan⁻¹ (tan x) = tan⁻¹ (15/12)

x = tan⁻¹ (15/12)

x = 51.34

This would be half of the angle at the top of the frame; this means the total angle would be 51.34+51.34 = 102.68. This makes the triangle an obtuse angle.