Question

Pythagorean theorem pls help :P

Answer 1

Answer:

A) $\sqrt{146}$

Step-by-step explanation:

The Pythagorean Theorem states that for a right triangle with side lengths $a$ and $b$, and a hypotenuse of $c$, the equation that relates to every side of the triangle is $a^2+b^2=c^2$.

In this case, we'll let $a=\sqrt{82}\:\text{mi}$ and $b=8\:\text{mi}$, and we can solve for the hypotenuse $x$:

$a^2+b^2=c^2\\\\\sqrt{82}^2+8^2=x^2\\\\82+64=x^2\\\\146=x^2\\\\\sqrt{146}=x$

Therefore, the missing side of the triangle is $\sqrt{146}\: \text{mi}$.

Answer 2

Answer:

$\sqrt{146}$

$\sqrt{\sqrt{82}^2 + 8^2} = \sqrt{146} (12.08)$