Find Missing Side of a Right Triangle

Pythagorean Theorem:

\[ \text{hypotenuse}^2 = \text{leg}_1^2 + \text{leg}_2^2 \]

\[ \text{Missing side} = \sqrt{\text{hyp}^2 - \text{leg}^2} \]

Missing Side (meters):

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1. What is the Missing Side Calculator?

Definition: This calculator finds the length of the missing side in a right triangle when you know the hypotenuse and one leg.

Purpose: It helps students, engineers, and DIYers solve right triangle problems quickly and accurately.

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem:

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

Where:

\( c \) — Hypotenuse (longest side)
\( a \) and \( b \) — Legs of the triangle

Explanation: When one leg is missing, we rearrange the formula:

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

3. Importance of Right Triangle Calculations

Details: Right triangle calculations are fundamental in construction, navigation, engineering, and many STEM fields.

4. Using the Calculator

Tips: Enter the hypotenuse and one known leg in meters. The hypotenuse must be longer than the known leg.

5. Frequently Asked Questions (FAQ)

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

Q2: What units should I use?
A: The calculator uses meters, but any consistent unit will work as long as you use the same unit for all sides.

Q3: Why does my calculation show an error?
A: Ensure the hypotenuse is longer than the known leg, and all values are positive numbers.

Q4: Can I use this for non-right triangles?
A: No, this calculator only works for right triangles. For other triangles, you would need the Law of Cosines.

Q5: How accurate are the results?
A: Results are accurate to three decimal places, sufficient for most practical applications.