How do you find the leg in a right triangle if one of the legs is in square root form?

Answer 1

In order to calculate either of the two legs or the hypotenuse of a Right Triangle, you will need to use the Pythagorean Theorem.

Pythagorean Theorem: A2 + B2 = C2

If you're working with a value that is already squared, then you'll need to square it again, in order to make the Pythagorean Theorem work.

Equation: (A2) + [(x2)2] = (C2) {Note: B = (x2)}

When simplified: (A2) + (x4) = (C2)

Suppose you have one leg with a length of 3 and a hypotenuse with a length of 5. Your remaining leg has a length of x2.

If you plug these numbers into the Pythagorean Theorem, you'll notice an equation like this:

32 + (x2)2 = 52 {Note: x2 = B}

Simplified:

9 + x4 = 25

[(9 + x4) - 9] = (25 - 9)

x4 = 16

{Note: sqrt means Square Root}

[sqrt(sqrt(x4))] = sqrt(sqrt(16))

x = sqrt(sqrt(16)) = 2

In other words, the square root of the square root of 16, equals 2. So, if the square of 2 is 4, then the square of 4 is 16.

Therefore, 32 + (22)2 = 52

OR

9 + (2*2)(2*2) = 25

OR

9 + 4*4 = 25

OR

9 + 16 = 25 {<- This is your answer to the Pythagorean Theorem}

OR

[(9 + 16) - 9] = (25 - 9)

OR

16 = 16 {proof your calculations are correct}