1. What is Height of Equilateral Triangle given Length of Angle Bisector?

The Height of an Equilateral Triangle given Length of Angle Bisector is a perpendicular line drawn from any vertex to the opposite side, calculated using the length of the angle bisector. In an equilateral triangle, the height, median, and angle bisector from any vertex coincide and have equal lengths.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( h \) — Height of Equilateral Triangle (m)
• \( l_{Angle\ Bisector} \) — Length of Angle Bisector of Equilateral Triangle (m)

Explanation: In an equilateral triangle, the height is equal to the length of the angle bisector, making the calculation straightforward with a division by 1.

3. Importance of Height Calculation

Details: Calculating the height of an equilateral triangle is essential in geometry for determining area, understanding triangle properties, and applications in various fields such as architecture and engineering.

4. Using the Calculator

Tips: Enter the length of the angle bisector in meters. The value must be valid (greater than 0).

5. Frequently Asked Questions (FAQ)

Q1: Why is the height equal to the angle bisector in an equilateral triangle?
A: In an equilateral triangle, all medians, altitudes, and angle bisectors coincide and are equal in length due to symmetry.

Q2: Can this formula be used for other types of triangles?
A: No, this specific relationship only holds true for equilateral triangles where all sides and angles are equal.

Q3: What are the units for height and angle bisector length?
A: Both are measured in meters (m), but any consistent unit of length can be used.

Q4: How accurate is this calculation?
A: The calculation is mathematically exact for equilateral triangles, provided the input is accurate.

Q5: Are there alternative methods to find the height?
A: Yes, the height can also be calculated using the side length with the formula \( h = \frac{\sqrt{3}}{2} \times side \).