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? \\bigcirc it is an acute triangle. about 0.8 foot needs to be removed from the 20 - foot board to create a right triangle. \\bigcirc it is an obtuse triangle. about 0.8 foot needs to be removed from the 20 - foot board to create a right triangle. \\bigcirc it is an acute triangle. about 7 feet need to be removed from the 20 - foot board to create a right triangle. \\bigcirc 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? \\bigcirc it is an acute triangle. about 0.8 foot needs to be removed from the 20 - foot board to create a right triangle. \\bigcirc it is an obtuse triangle. about 0.8 foot needs to be removed from the 20 - foot board to create a right triangle. \\bigcirc it is an acute triangle. about 7 feet need to be removed from the 20 - foot board to create a right triangle. \\bigcirc 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: Check triangle type (Pythagorean theorem)

For a right triangle with legs (a = 12), (b = 15), hypotenuse (c) should be (c=\sqrt{12^{2}+15^{2}}=\sqrt{144 + 225}=\sqrt{369}\approx19.21). The given support beam is 20 ft, which is longer than 19.21 ft. In a triangle, if (c^{2}>a^{2}+b^{2}), it's obtuse. Here, (20^{2}=400), (12^{2}+15^{2}=369), so (400>369) → obtuse triangle.

Step2: Find length to remove

Difference between 20 and 19.21: (20 - 19.21\approx0.8) foot. So we remove ~0.8 ft from 20 - ft board.

Answer:

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