Question 1

What is the hypotenuse?

Accepted Answer

The hypotenuse is the longest side of a right triangle, opposite the right angle. In the Pythagorean theorem formula a² + b² = c², the hypotenuse is represented by c.

Question 2

When does the Pythagorean theorem apply?

Accepted Answer

The Pythagorean theorem applies only to right triangles (triangles with one 90-degree angle). It states that the square of the hypotenuse equals the sum of squares of the two legs: a² + b² = c².

Question 3

What are real-life applications of the Pythagorean theorem?

Accepted Answer

The Pythagorean theorem is used in construction (ensuring square corners), navigation (calculating distances), engineering (designing structures), computer graphics (calculating distances), and many other fields where right triangles appear.

Question 4

How do I find the hypotenuse?

Accepted Answer

To find the hypotenuse, you need to know both legs (a and b). Use the formula c = √(a² + b²). Enter both leg lengths in the calculator and select 'Find Hypotenuse' mode.

Question 5

How do I find a missing leg?

Accepted Answer

To find a missing leg, you need to know the hypotenuse (c) and the other leg (a). Use the formula b = √(c² − a²). Enter the hypotenuse and known leg, then select 'Find Missing Leg' mode.

Question 6

What units should I use?

Accepted Answer

You can use any unit of length (cm, m, inches, feet, etc.). The result will be in the same units as your input. For example, if you enter dimensions in meters, the result will be in meters.

Question 7

How accurate are the calculations?

Accepted Answer

The calculator uses standard mathematical formulas with high precision. Results are rounded to 6 decimal places for display. The calculations are mathematically exact for the given inputs.

Question 8

What if I enter negative numbers?

Accepted Answer

All side lengths must be positive numbers greater than zero. The calculator will validate inputs and show an error if invalid values are entered. Triangle sides cannot be negative or zero.

Question 9

Why must the hypotenuse be greater than the leg?

Accepted Answer

In a right triangle, the hypotenuse is always the longest side (opposite the right angle). Therefore, when finding a missing leg, the hypotenuse c must be greater than the known leg a, otherwise the triangle cannot exist.

Question 10

Can I use this for non-right triangles?

Accepted Answer

No, the Pythagorean theorem applies only to right triangles. For other triangles, you would need different formulas such as the Law of Cosines or Law of Sines.

Question 11

What are Pythagorean triples?

Accepted Answer

Pythagorean triples are sets of three positive integers (a, b, c) that satisfy a² + b² = c². Common examples include (3, 4, 5), (5, 12, 13), (8, 15, 17), and (7, 24, 25).

Question 12

How do I verify my calculation?

Accepted Answer

You can verify by checking if a² + b² = c². For example, if you calculated c=5 from a=3 and b=4, verify: 3² + 4² = 9 + 16 = 25 = 5². The calculator shows the formula with substituted values for easy verification.

Pythagorean Theorem Calculator

Calculator

How to Calculate

Examples

Example 1: Find hypotenuse (a=3, b=4)

Example 2: Find hypotenuse (a=5, b=12)

Example 3: Find missing leg (c=10, a=6)

Example 4: Find missing leg (c=15, a=9)

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