1. What is an Equilateral Triangle?

An equilateral triangle is a special type of triangle where all three sides are equal in length and all three angles are 60 degrees. It's a regular polygon with three sides.

2. Height Calculation Formula

The formula to calculate the height (h) of an equilateral triangle with side length (s) is:

Where:

• \( h \) — Height of the triangle (units)
• \( s \) — Length of one side (units)
• \( \sqrt{3}/2 \) — Constant ratio (≈0.866)

Derivation: The height forms a right triangle that divides the equilateral triangle into two 30-60-90 triangles, allowing us to use the properties of these special right triangles.

3. Practical Applications

Details: Knowing the height of an equilateral triangle is essential in architecture, engineering, and design when working with triangular structures or components.

4. Using the Calculator

Tips: Simply enter the length of one side of the equilateral triangle. The calculator will compute the height automatically. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How is this different from other triangle height calculations?
A: For equilateral triangles, the height can be calculated directly from the side length using this simple formula, unlike other triangles which require more information.

Q2: Can I calculate the side length if I know the height?
A: Yes, you can rearrange the formula: \( s = \frac{2h}{\sqrt{3}} \).

Q3: What's the relationship between height and area?
A: The area of an equilateral triangle can be calculated as \( \frac{\sqrt{3}}{4} \times s^2 \) or \( \frac{h \times s}{2} \).

Q4: Are all heights equal in an equilateral triangle?
A: Yes, all three heights (from each vertex to the opposite side) are equal in length in an equilateral triangle.

Q5: How precise is this calculation?
A: The calculation is mathematically exact. Any imprecision would come from measurement of the side length or rounding of results.