Sides of a 90 Degree Triangle Calculator

Pythagorean Theorem:

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

Unknown Leg (a):

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1. What is a 90 Degree Triangle Calculator?

Definition: This calculator determines the length of an unknown side in a right-angled triangle using the Pythagorean theorem.

Purpose: It helps students, engineers, and construction professionals quickly solve for missing sides in right triangles.

2. How Does the Calculator Work?

The calculator uses the formula:

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

Where:

\( a \) — Unknown leg (units)
\( b \) — Known leg (units)
\( c \) — Hypotenuse (units)

Explanation: The square of the hypotenuse equals the sum of the squares of the other two sides in a right triangle.

3. Importance of Right Triangle Calculations

Details: Accurate triangle calculations are essential in construction, navigation, engineering, and various STEM fields.

4. Using the Calculator

Tips: Enter the hypotenuse and one leg length. Both values must be positive numbers, and the 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, not the hypotenuse.

Q2: What units should I use?
A: Any consistent unit (meters, feet, inches, etc.). The result will be in the same units as your input.

Q3: Why does the hypotenuse need to be longer than the leg?
A: By definition, the hypotenuse is always the longest side in a right triangle.

Q4: What if I get an error message?
A: Check that: 1) Your hypotenuse > leg, 2) Both values > 0, 3) You've entered numbers in both fields.

Q5: Can this calculate angles too?
A: No, this only calculates side lengths. For angles, you'd need trigonometric functions (sine, cosine, tangent).