Question

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

Explanation:

Step1: Apply Pythagorean theorem

In a right - triangle, $a^{2}+b^{2}=c^{2}$, where $c$ is the hypotenuse and $a$ and $b$ are the legs. Here, $c = 80$ m and $a = 64$ m. We want to find $b$. So, $b=\sqrt{c^{2}-a^{2}}$.

Step2: Substitute values

$b=\sqrt{80^{2}-64^{2}}=\sqrt{(80 + 64)(80 - 64)}$ (using the difference - of - squares formula $x^{2}-y^{2}=(x + y)(x - y)$). First, $80+64 = 144$ and $80 - 64 = 16$. Then $b=\sqrt{144\times16}$.

Step3: Calculate square roots

$\sqrt{144\times16}=\sqrt{144}\times\sqrt{16}$. Since $\sqrt{144}=12$ and $\sqrt{16}=4$, $b = 12\times4=48$ m.

Answer:

48