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

`AB=5√(15)\ units`

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=√(375)\ units`

simplify

we know that

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

substitute

`AB=√(5^2(15))\ units`

`AB=5√(15)\ units`