Pythagorean Theorem Calculation

1. The right triangle you want to find is known. Enter the length of the two sides.
2. The remaining side length that you did not enter will be calculated automatically.
3. Also, the "angle" and "area" are calculated at the same time.

Pythagorean theorem The Pythagorean theorem is a fundamental mathematical theorem about the lengths of the sides of right-angled triangles.

The Pythagorean theorem has been known since ancient times, and was known to ancient Babylonians and Indian mathematicians. It was named after the ancient Greek mathematician Pythagoras, who systematized it.

Contents of the theorem

In a right-angled triangle, the hypotenuse The square of the length of is equal to the sum of the squares of the lengths of the other two sides.

c² = a² + b²

• c: Hypotenuse (the side that is closest to the right angle long side)
• a: other side
• b: Another side

Integer values ​​for finding right-angled triangles (Pythagorean numbers)

The following combinations of integers satisfy Pythagorean theorem. < /p>

• 3,4,5
• 5,12,13
• 7,24,25

Find the hypotenuse (c)

c = √(a² + b²)

Calculation example

When a = 3, b = 4

c = √(3² + 4²) = √(9 + 16) = √25 = 5

Find the length of one side (a)

a = √(c² − b²)

Example calculation

a = √(10² − 6²) = √(100 − 36) = √64 = 8

One side (b) Required

b = √(c² − a²)

Calculation example

c = 13,a = 5 In this case, b = √(13² − 5²) = √(169 − 25) = √144 = 12. Calculate the area. S = a × b / 2

Angle calculation

θ = tan^-1(b/a)