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. 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:

Step1: Analyze direction

Lin walked west from house to lecture - hall, then northeast from lecture - hall to gym. To get back to the house from the gym, considering the previous directions, he must walk southwest.

Step2: Check triangle type

Let \(a = 615\), \(b = 651\), \(c = 910\). Use the Pythagorean theorem's converse \(c^{2}=a^{2}+b^{2}\) for right - triangle, \(c^{2}>a^{2}+b^{2}\) for obtuse - triangle and \(c^{2}a^{2}+b^{2}\), it is an obtuse - triangle.

Answer:

Lin walked southwest, creating an obtuse triangle.