Question

What is the length of the hypotenuse of the triangle?

what is the length of the hypotenuse of the triangle?


what is the length of the hypotenuse of the triangle?


triangle a b c. side a c is 7 feet and side c b is 4 feet. hypotenuse a b is unknown.
startroot 22 endroot ft
startroot 33 endroot ft
startroot 57 endroot ft
startroot 65 endroot ft

Answer 1

$\textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies c=\sqrt{a^2 + b^2} \qquad \begin{cases} c=hypotenuse\\ a=\stackrel{adjacent}{7}\\ b=\stackrel{opposite}{4}\\ \end{cases} \\\\\\ c=\sqrt{7^2 + 4^2}\implies c=\sqrt{65}$