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: Recall triangle - type rules

In a right - triangle, \(a^{2}+b^{2}=c^{2}\), in an acute - triangle \(a^{2}+b^{2}>c^{2}\), and in an obtuse - triangle \(a^{2}+b^{2}

Step2: Identify the side lengths

Let \(a = 615\), \(b = 651\), and \(c = 910\).

Step3: Calculate \(a^{2}+b^{2}\) and \(c^{2}\)

\(a^{2}=615^{2}=378225\), \(b^{2}=651^{2}=423801\). Then \(a^{2}+b^{2}=378225 + 423801=802026\). And \(c^{2}=910^{2}=828100\).
Since \(a^{2}+b^{2}=802026<828100 = c^{2}\), the triangle is obtuse.
The direction from the gym to the house is southwest.

Answer:

Lin walked southwest, creating an obtuse triangle.