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 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 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.

Explanation:

Step1: Apply Pythagorean theorem

Let \(a = 12\), \(b=15\). For a right - triangle, the length of the hypotenuse \(c\) should satisfy \(c=\sqrt{a^{2}+b^{2}}\).
\[c=\sqrt{12^{2}+15^{2}}=\sqrt{144 + 225}=\sqrt{369}\approx19.2\]

Step2: Analyze the current triangle

The actual length of the support beam is \(20\) feet. Since \(20>19.2\), by the converse of the Pythagorean theorem, the triangle is an obtuse - triangle.

Step3: Calculate the amount to be removed

The amount 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.