Question

applying triangle classification theorems
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.
lecture hall 651 ft lins house
gym 910 ft 615 ft

Explanation:

Step1: Identify side lengths

Let $a=615$, $b=651$, $c=910$

Step2: Test right triangle condition

Check if $a^2 + b^2 = c^2$:

$$\begin{align*} 615^2 + 651^2 &= 378225 + 423801 \\ &= 802026 \end{align*}$$

$$\begin{align*} 910^2 &= 828100 \end{align*}$$

Step3: Compare values for triangle type

Since $a^2 + b^2 < c^2$, the triangle is obtuse.

Step4: Determine direction

From gym to house, opposite of northeast is southwest.

Answer:

Lin walked southwest, creating an obtuse triangle.