Question

practice: pythagorean theorem & ratios
solve for the missing side using pythagorean theorem:
1.
right triangle with legs 9 and 12, hypotenuse c
2.
right triangle with leg 24, hypotenuse 25, leg b
3.
right triangle with leg 39, hypotenuse 89, leg a
5.
(note: the top part of the image has a right triangle with leg b, and the formulas $a^2 + b^2 = c^2$ or $b^2 = c^2 - a^2$)

Explanation:

Step1: Substitute values for triangle 1

$a=9$, $b=12$, use $c^2=a^2+b^2$
$c^2=9^2+12^2=81+144=225$

Step2: Solve for $c$ (triangle 1)

$c=\sqrt{225}=15$

Step3: Substitute values for triangle 2

$c=25$, $a=24$, use $b^2=c^2-a^2$
$b^2=25^2-24^2=625-576=49$

Step4: Solve for $b$ (triangle 2)

$b=\sqrt{49}=7$

Step5: Substitute values for triangle 3

$c=89$, $b=39$, use $a^2=c^2-b^2$
$a^2=89^2-39^2=7921-1521=6400$

Step6: Solve for $a$ (triangle 3)

$a=\sqrt{6400}=80$

Answer:

1. $c=15$
2. $b=7$
3. $a=80$