Question

o get from his house to the lecture hall at school, Lin walked west 651 feet. After class, he walked northeast 910 feet to the gym. Finally, he walked 615 feet back to his house from the gym. A triangle has points gym, Lin apostrophe s house, and lecture hall. The distance between the lecture hall and gym is 910 feet. The distance between the gym and Lin apostrophe s house is 615 feet. The distance between the lecture hall and Lin apostrophe s house is 651 feet. What general direction did Lin walk from the gym to his house, and what type of triangle did his walking path form? Lin walked south, creating a right triangle. Lin walked southwest, creating an obtuse triangle. Lin walked southeast, creating an acute triangle. Lin walked directly east, creating a right triangle.

Answer 1

Answer:

Lin walked southwest, creating an obtuse triangle.

Step-by-step explanation:

The triangle has sides of lengths 651 ft, 615 ft, and 910 ft.

If this were a right triangle, then the Pythagorean theorem would have to work. If tis were a right triangle, the the two shorter sides would be the legs forming the right angle.

a^2 + b^2 = c^2

615^2 + 651^2 = 378225 + 432801 = 802026

sqrt(802026) = 896

Since the calculation of the length of the hypotenuse for a right angle is 896 ft, but the actual third side is 910 feet, then this is not a right triangle. In addition, in order to accommodate a longer third side, you'd have to open up the angle a bit making it an obtuse angle. This is an obtuse triangle.

Answer: Lin walked southwest, creating an obtuse triangle.