Question

HELP PLEASE
Find the value of x, if you know the hypotenuse is 10 and 1 of the sides is 5. X is the other side.

Answer 1

We can use Pythagorean's Theorem to solve for the unknown side:
$a^2+b^2=c^2$

Solve for b (c is the hypotenuse and it doesn't matter which side is a or b):
$b = \sqrt{c^2-a^2} = \sqrt{10^2-5^2} = \sqrt{100-25} = \sqrt{75}$

We can simplify this:
$\sqrt{75} = \sqrt{25*3} = 5 \sqrt{3}$

So, your answer is, b = $5 \sqrt{3}$

Answer 2

Hey there! :) 

For questions like these, where you are given the hypotenuse & one side of a triangle, then we can very simply use the Pythagorean Theorem to find x.

Pythagorean Theorem : a² + b² = c²

Where :

a = side length 
b = another side length
c = hypotenuse

Since we are given 10 as the hypotenuse and 5 as a side length, we can very simply plug these into the Pythagorean theorem. 

a² + b² = c²

We'll plug 10 into 'c' and 5 into 'a.'

(5²) + b² = (10²)

Simplify.

25 + b² = 100

Now, subtract 25 from both sides.

b² = 100 - 25

Simplify.

b² = 75

Now, find the square root of b² and 75.

$\sqrt{b^2} = \sqrt{75}$

Simplify.

$b = 5 \sqrt{3}$

Therefore, our final side length is : $5 \sqrt{3}$

~Hope I helped!~