arielle is building the wooden framework for the roof of a house. she needs the angle created by the…

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.

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

Explanation:

Step1: Apply Pythagorean theorem

Let the vertical side $a = 12$ feet and the horizontal side $b=15$ feet. In a right - triangle, the length of the hypotenuse $c$ should satisfy $c=\sqrt{a^{2}+b^{2}}$. So $c=\sqrt{12^{2}+15^{2}}=\sqrt{144 + 225}=\sqrt{369}\approx19.2$ feet.

Step2: Determine triangle type

The actual length of the support beam is 20 feet. Since $20^{2}=400$, $12^{2}+15^{2}=369$, and $20^{2}>12^{2}+15^{2}$, by the converse of the Pythagorean theorem, the triangle is obtuse.

Step3: Calculate length to be removed

The length to be removed from the 20 - foot board to make it a right - triangle is $20 - 19.2=0.8$ feet.

Answer:

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