Question

eighth grade t.3 pythagorean theorem: find the missin... mtm questions time smartscore 1 00:30 10 video 39 mi. a 15 mi. what is the length of the missing leg? if necessary, round to the nearest tenth. a = miles

Explanation:

Step1: Recall 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, $c = 39$ mi and $b = 15$ mi, and we want to find $a$. So, $a=\sqrt{c^{2}-b^{2}}$.

Step2: Substitute values

Substitute $c = 39$ and $b = 15$ into the formula: $a=\sqrt{39^{2}-15^{2}}=\sqrt{(39 + 15)(39 - 15)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, calculate $39+15 = 54$ and $39 - 15 = 24$. Then $a=\sqrt{54\times24}=\sqrt{1296}$.

Step3: Calculate the square - root

$\sqrt{1296}=36$.

Answer:

36