Question

1. state if the three side lengths form an acute, obtuse, or right triangle. 6 mi, 2\sqrt{55} mi, 17 mi

Explanation:

Step1: Identify the longest side

The longest side is $c = 17$ mi, and the other two sides are $a = 6$ mi and $b=2\sqrt{55}$ mi.

Step2: Calculate $a^{2}+b^{2}$ and $c^{2}$

First, calculate $a^{2}=(6)^{2}=36$, $b^{2}=(2\sqrt{55})^{2}=4\times55 = 220$. Then $a^{2}+b^{2}=36 + 220=256$. And $c^{2}=(17)^{2}=289$.

Step3: Compare $a^{2}+b^{2}$ and $c^{2}$

Since $a^{2}+b^{2}=256$ and $c^{2}=289$, and $a^{2}+b^{2}

Answer:

Obtuse triangle