Find Missing Side of Right Triangle

Pythagorean Theorem:

\[ a^2 + b^2 = c^2 \]

\[ \text{missing leg} = \sqrt{c^2 - a^2} \]

Missing Leg (b):

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1. What is the Missing Side Calculator?

Definition: This calculator finds the length of the missing leg in a right triangle using the Pythagorean theorem.

Purpose: It helps students, engineers, and DIYers quickly determine the unknown side of a right triangle when two sides are known.

2. How Does the Calculator Work?

The calculator uses the formula:

\[ b = \sqrt{c^2 - a^2} \]

Where:

\( b \) — Missing leg (meters)
\( c \) — Hypotenuse (meters)
\( a \) — Known leg (meters)

Explanation: The square of the hypotenuse minus the square of the known leg equals the square of the missing leg.

3. Importance of Right Triangle Calculations

Details: Right triangle calculations are fundamental in construction, navigation, physics, and many engineering applications.

4. Using the Calculator

Tips: Enter the hypotenuse and one leg length in meters. Both values must be positive, and the hypotenuse must be longer than the leg.

5. Frequently Asked Questions (FAQ)

Q1: What if I know two legs but not the hypotenuse?
A: Use \( c = \sqrt{a^2 + b^2} \) to find the hypotenuse instead.

Q2: What units does this calculator use?
A: The default is meters, but any consistent unit can be used (cm, ft, etc.).

Q3: Why does the hypotenuse need to be longer than the leg?
A: In a right triangle, the hypotenuse is always the longest side (opposite the 90° angle).

Q4: What if I get an error message?
A: Check that your hypotenuse is longer than the known leg and both values are positive.

Q5: Can this be used for non-right triangles?
A: No, you would need the Law of Cosines or Law of Sines for other triangles.