i need help please thank you

hi! so this looks like a right triangle because it has a right angle which is 90 degrees! that means we can use the Pythagorean theorem to solve for the missing leg.

The Pythagorean theorem: [tex]a^{2} + b^{2} = c^{2}[/tex]

a and b will be the two shorter legs, so it does not matter which of the two legs are which! in this problem, 5 and b (the missing leg) are the two shorter legs!
c is always the hypotenuse, which is the sloped-looking line. in this problem, 13 is the hypotenuse! this line is the longest side on every right triangle!

Let's solve for the missing leg now!

1) first, we need to plug in the missing numbers into the equation

[tex]5^{2} + b^{2} = 13^{2}[/tex]

2) next, let's simplify the problem

[tex]25 + b^{2} = 169[/tex]

3) now, let's isolate the variable, b

[tex]b^{2} = 144[/tex]

4) finally, we have to take the square root of b so it will be b not [tex]b^{2}[/tex]

b = 12

Let's plug in our answer to the equation to check if it is correct!

[tex]5^{2} + 12^{2} = 13^{2}[/tex]

25 + 144 = 169

169 = 169 hooray!

you do not have to do all of this work if you memorize the Pythagorean triples!

(3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17) , (9, 40, 41)
these are automatic matches!
for example: [tex]3^{2} + 4^{2} = 5^{2} --> 9 + 16 = 25 --> 25 = 25[/tex]

comment or message if you have any questions :)