Question

what is the length of the missing leg? if necessary, round to the nearest tenth. a = kilometers

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $c^{2}=a^{2}+b^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here, $c = 5$ km and $b = 2$ km. We want to find $a$, so $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

Substitute $c = 5$ and $b = 2$ into the formula: $a=\sqrt{5^{2}-2^{2}}=\sqrt{25 - 4}=\sqrt{21}$.

Step3: Calculate and round

$\sqrt{21}\approx4.6$ km.

Answer:

$4.6$