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? \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.

Explanation:

Step1: Identify right triangle hypotenuse

Use Pythagorean theorem for right triangle with legs 12 ft and 15 ft:
$$c = \sqrt{12^2 + 15^2}$$
$$c = \sqrt{144 + 225} = \sqrt{369} \approx 19.21 \text{ feet}$$

Step2: Classify current triangle

Compare $20^2$ with $12^2 + 15^2$:
$$20^2 = 400, \quad 12^2 + 15^2 = 369$$
Since $400 > 369$, the triangle is obtuse.

Step3: Calculate length to remove

Subtract ideal hypotenuse from 20 ft:
$$20 - 19.21 = 0.79 \approx 0.8 \text{ feet}$$

Answer:

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