How To Calculate Height

Pythagorean Theorem:

\[ \text{height} = \sqrt{\text{diagonal}^2 - \text{width}^2} \]

Height:

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1. What is the Pythagorean Theorem?

The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides. This calculator applies this theorem to find the height when you know the diagonal and width.

2. How Does the Calculator Work?

The calculator uses the Pythagorean theorem rearranged to solve for height:

\[ \text{height} = \sqrt{\text{diagonal}^2 - \text{width}^2} \]

Where:

\( \text{diagonal} \) — The hypotenuse or diagonal measurement
\( \text{width} \) — One side of the right triangle
\( \text{height} \) — The unknown side we're calculating

Explanation: The theorem relates the three sides of a right triangle, allowing us to calculate any side when we know the other two.

3. Practical Applications

Details: This calculation is useful in many real-world scenarios like determining TV screen height from its diagonal and width, calculating ladder reach, or finding the height of a rectangular space when you know its diagonal measurement.

4. Using the Calculator

Tips: Enter the diagonal and width in the same units (both in inches, centimeters, etc.). The diagonal must be longer than the width for a valid result. Both values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: Why must the diagonal be longer than the width?
A: In a right triangle, the hypotenuse (diagonal) is always the longest side. If width were equal to or longer than the diagonal, we wouldn't have a valid right triangle.

Q2: Can I use this for non-rectangular shapes?
A: This specifically calculates the height of a right triangle or rectangle when you know the diagonal and width. It doesn't apply to other shapes.

Q3: What if I get an error message?
A: Check that your diagonal is larger than your width and that both values are positive numbers. The calculator will show an error if these conditions aren't met.

Q4: How precise are the results?
A: Results are precise to two decimal places. For most practical applications, this is sufficient precision.

Q5: Can I calculate width if I know height and diagonal?
A: Yes, you would use a similar formula: width = √(diagonal² - height²). The same mathematical principle applies.