Question

85 km
77 km
what is the length of the missing leg? if necessary, round to the nearest tenth.
b = \boxed{} kilometers

Explanation:

Step1: Identify the triangle type

This is a right - triangle, so we can use the Pythagorean theorem. The Pythagorean theorem is $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse (the longest side), and $a$ and $b$ are the legs. Here, $c = 85$ km and one leg $a=77$ km, and we need to find the other leg $b$.

Step2: Rearrange the Pythagorean theorem

We can rearrange the formula to solve for $b$: $b^{2}=c^{2}-a^{2}$.
Substitute $c = 85$ and $a = 77$ into the formula:
$b^{2}=85^{2}-77^{2}$
First, calculate $85^{2}=85\times85 = 7225$ and $77^{2}=77\times77=5929$.
Then, $b^{2}=7225 - 5929=1296$.

Step3: Solve for b

Take the square root of both sides: $b=\sqrt{1296}$.
Since $\sqrt{1296} = 36$, we get $b = 36$.

Answer:

36