Question

what is the length of the unlabeled side?
A- 5 in
B- 7 in
C- 16 in
D- 25 in

Answer 1

Hello there,

We can use the Pythagorean theorem. This is a²+b²=c²

So let's break this down. C is the hypotenuse. That is 13.
We will use b for 12 you can also use a it doesn't really matter.

So this turns into a²+(12)²=(13)²
Which equals a²+144=169
Subtract 144
You get a²=25
Now to get rid of the squared, you square root the a and the 25 so it becomes just an a.
This brings us to a=√25
Which means a=5

So A Is your answer.

Hope this helped you!

Answer 2

In order to solve this, we will need to use Pythagoras' Theorem:

$c^{2} = a^{2} + b ^{2}$

However, since we are trying to find the shorter side, we need to rearrange the formula:

$a^{2} = c^{2} - b^{2}$

In this case, c = 13in (hypotenuse)  
                    b = 12in

Sub these values to find a,

$a^{2} = 13^{2} - 12^{2}$
$a^{2}$ = 25

Square root both sides to get 'a' on its own,

a = 5

Therefore, the unknown side is 5in!

Hope this helped! Ask me if there's any part of the working you don't understand :)