Question

example
using the theorem, you know $3^2 + 4^2 = c^2$
$9 + 16 = c^2$
$25 = c^2$
$sqrt{25} = c$
$5 = c$

using the pythagorean theorem, calculate the value of the

1. right triangle with legs 9cm and 12cm, find hypotenuse $c$
2. right triangle with legs 15cm and 20cm, find hypotenuse $c$
3. right triangle with hypotenuse 78cm and one leg 30cm, find side $b$
4. right triangle with hypotenuse 51cm and one leg 45cm, find side $a$

Explanation:

Step1: Apply Pythagorean theorem

For first triangle: $c^2 = 9^2 + 12^2$

Step2: Calculate squares

$c^2 = 81 + 144 = 225$

Step3: Solve for c

$c = \sqrt{225} = 15\mathrm{cm}$

Step1: Apply Pythagorean theorem

For second triangle: $c^2 = 15^2 + 20^2$

Step2: Calculate squares

$c^2 = 225 + 400 = 625$

Step3: Solve for c

$c = \sqrt{625} = 25\mathrm{cm}$

Step1: Apply Pythagorean theorem

For third triangle: $b^2 = 78^2 - 30^2$

Step2: Calculate squares

$b^2 = 6084 - 900 = 5184$

Step3: Solve for b

$b = \sqrt{5184} = 72\mathrm{cm}$

Step1: Apply Pythagorean theorem

For fourth triangle: $a^2 = 51^2 - 45^2$

Step2: Calculate squares

$a^2 = 2601 - 2025 = 576$

Step3: Solve for a

$a = \sqrt{576} = 24\mathrm{cm}$

Answer:

1. $c=15\mathrm{cm}$
2. $c=25\mathrm{cm}$
3. $b=72\mathrm{cm}$
4. $a=24\mathrm{cm}$