Pythagorean Theorem Calculator
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Pythagorean Theorem Calculator
a² + b² = c² (find any missing side)
How to Use This Calculator
The calculator takes two inputs: the lengths of the two sides of a right-angled triangle that form the right angle. These sides are often called the base and height. For example, if you enter 3 for the base and 4 for the height, the calculator will output the length of the hypotenuse.
A worked example: if you enter 5 for the base and 12 for the height, the calculator will output the length of the hypotenuse, which is approximately 13.
The Formula Behind It
The formula is a^2 + b^2 = c^2, where a and b are the lengths of the two sides that form the right angle, and c is the length of the hypotenuse.
- a is the length of one side of the triangle
- b is the length of the other side of the triangle
- c is the length of the hypotenuse, which is the side opposite the right angle.
Practical Examples
- If a building has a shadow of 10 meters and the angle of elevation of the sun is such that the height of the building forms a right-angled triangle with the shadow, and the height is 8 meters, the calculator will output the length of the hypotenuse, which is approximately 12.8 meters.
- A right-angled triangle has one side of 6 meters and the other of 8 meters. The calculator will output the length of the hypotenuse, which is approximately 10 meters.
- A ladder of 15 meters is placed against a wall, forming a right-angled triangle with the wall and the ground. If the ladder is 12 meters away from the wall, the calculator will output the height of the wall, which is approximately 9.5 meters, using the reverse calculation.
Common Questions
What is the Pythagorean theorem used for?
The Pythagorean theorem is used to find the length of the hypotenuse of a right-angled triangle, given the lengths of the other two sides.
Can I use this calculator for non-right angled triangles?
No, this calculator only works for right-angled triangles.
What if I only know the length of one side and the hypotenuse?
You can rearrange the formula to solve for the other side.
Can I use this calculator for 3D triangles?
No, this calculator only works for 2D triangles.
Are the results always exact?
No, the results may be approximate due to the way the calculator performs calculations.