1. What is the Isosceles Triangle Sides Formula?

The formula calculates the length of the equal sides (legs) of an isosceles triangle when you know the height and base length. It's derived from the Pythagorean theorem applied to one of the two right triangles formed by the height.

2. How Does the Calculator Work?

The calculator uses the following formula:

Where:

• \( a \) — Length of the equal sides (legs)
• \( h \) — Height of the isosceles triangle
• \( b \) — Base length of the triangle

Explanation: The height divides the isosceles triangle into two congruent right triangles, allowing us to apply the Pythagorean theorem to find the side length.

3. Importance of Side Length Calculation

Details: Calculating side lengths is essential in geometry, construction, and design where precise measurements of triangular components are needed.

4. Using the Calculator

Tips: Enter the height and base length in the same units. Both values must be positive numbers. The calculator will return the length of the equal sides in the same units.

5. Frequently Asked Questions (FAQ)

Q1: Can this formula be used for all triangles?
A: No, this specific formula only works for isosceles triangles where two sides are equal.

Q2: What if I know the side length but need the height?
A: The formula can be rearranged to solve for height: \( h = \sqrt{a^2 - (b/2)^2} \)

Q3: Does this work for equilateral triangles?
A: Yes, since equilateral triangles are a special case of isosceles triangles where all sides are equal.

Q4: What units should I use?
A: Any consistent length units can be used (cm, inches, meters, etc.) as long as both inputs are in the same units.

Q5: How accurate is the calculation?
A: The calculation is mathematically exact, though practical accuracy depends on the precision of your input measurements.