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.

Explanation:

Step1: Use Pythagorean theorem

For a right - triangle with legs \(a = 12\) and \(b=15\), 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: Determine the length to be removed

The length of the support beam is \(20\) feet. The length to be removed is \(20 - 19.2=0.8\) feet.

Step3: Classify the triangle

Since \(12^{2}+15^{2}=144 + 225 = 369\) and \(20^{2}=400\), and \(12^{2}+15^{2}<20^{2}\). By the converse of the Pythagorean theorem, if \(a^{2}+b^{2}

Answer:

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