Missing Length of Right Triangle Calculator

Pythagorean Theorem:

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

Missing Leg (meters):

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1. What is a Missing Length of Right Triangle Calculator?

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

Purpose: It helps students, engineers, and construction professionals quickly find unknown side lengths in right-angled triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( a \) — Missing leg length (meters)
\( c \) — Hypotenuse length (meters)
\( b \) — Known leg length (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: Accurate triangle measurements are essential in construction, engineering, navigation, and various STEM fields.

4. Using the Calculator

Tips: Enter the hypotenuse and one leg length in meters. Both values must be positive, and hypotenuse must be longer than the 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. This calculator solves for a missing leg only.

Q2: What units does this calculator use?
A: The calculator uses meters, but the same formula works for any consistent unit of measurement.

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: 1) Values are positive, 2) Hypotenuse > leg, and 3) Both fields are filled.

Q5: How accurate are the results?
A: Results are accurate to 3 decimal places, sufficient for most practical applications.