Question

Given: ΔABC is a right triangle. AC = 20 BC = 5 Determine the length of the missing side of ΔABC. When applicable, simplify radicals and show all of your work.

Answer 1

Answer:

$AB=5\sqrt{15}\ units$

Step-by-step explanation:

we know that

In the right triangle ABC

we have

$AC=20\ units$ ----> is the hypotenuse

$BC=5\ units$ ----> is a leg

$AB=?\ units$ ----> is a leg

see the attached figure to better understand the problem

Applying the Pythagorean Theorem

$AC^2=AB^2+BC^2$

substitute the given values

$20^2=AB^2+5^2$

solve for AB

$AB^2=20^2-5^2$

$AB^2=375$

$AB=\sqrt{375}\ units$

simplify

we know that

$375=(25)(15)=5^2(15)$

substitute

$AB=\sqrt{5^2(15)}\ units$

$AB=5\sqrt{15}\ units$