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: Check the Pythagorean theorem

We know that for a right - triangle, \(a^{2}+b^{2}=c^{2}\), where \(c\) is the longest side. Let \(a = 615\), \(b=651\), and \(c = 910\).
Calculate \(a^{2}+b^{2}\):
\(615^{2}+651^{2}=615\times615 + 651\times651=378225+423801 = 802026\)
Calculate \(c^{2}\):
\(910^{2}=910\times910 = 828100\)
Since \(615^{2}+651^{2}<910^{2}\), by the converse of the Pythagorean theorem (\(a^{2}+b^{2}

Step2: Determine the direction

Lin walked from the gym to his house. If we consider the coordinate system (assuming Lin's house is to the right (east - west axis) and the gym is above (north - south axis) relative to the lecture hall). Since he is going from a point (gym) to a point (his house) which is to the lower - left (relative to the gym - lecture - hall - house coordinate), the general direction is southwest.

Answer:

Lin walked southwest, creating an obtuse triangle.