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.

The correct option is:

Lin walked southwest, creating an obtuse triangle.

This could be done by checking the property of Pythagorean Theorem as:

if c is the highest measure of a side then if a and b are the other sides of the triangle  then if:

The triangle is Right triangle.

The triangle is obtuse triangle.

The triangle is acute.

Here we have:

c=910 feet.

Let a=651 feet and b=615 feet.

so clearly,

So, clearly:

(615)^2+(651)^2" class="latex-formula" id="TexFormula8" src="https://tex.z-dn.net/?f=%28910%29%5E2%3E%28615%29%5E2%2B%28651%29%5E2" title="(910)^2>(615)^2+(651)^2">

Hence, the triangle so formed will be a obtuse triangle.

Also by the figure we could see that the direction is:

southwest.

Lin walked southwest, creating an obtuse triangle!!