Question

to 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.

image of a right triangle with vertices labeled lecture hall, lins house, and gym. the side from lecture hall to lins house is 651 ft, from lins house to gym is 615 ft, and from lecture hall to gym is 910 ft.

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.

Explanation:

1. Direction Analysis: From the gym to Lin's house, looking at the diagram, the path is downward (south) and to the left (west), so the general direction is southwest.
2. Triangle Type Analysis: First, check if it's a right triangle using the Pythagorean theorem. Calculate \(651^2 + 615^2\) and \(910^2\).

• \(651^2=651\times651 = 423801\)
• \(615^2=615\times615 = 378225\)
• Sum: \(423801 + 378225=802026\)
• \(910^2 = 828100\)

Since \(651^2+615^2=802026<910^2 = 828100\), by the converse of the Pythagorean theorem (if \(a^{2}+b^{2}

Answer:

Lin walked southwest, creating an obtuse triangle.