Calculate Height of Isosceles Triangle

Height Formula:

\[ h = \sqrt{leg^2 - \left(\frac{base}{2}\right)^2} \]

Height (h):

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1. What is the Height of an Isosceles Triangle?

The height (altitude) of an isosceles triangle is the perpendicular distance from the base to the opposite vertex. It divides the isosceles triangle into two congruent right triangles.

2. How Does the Calculator Work?

The calculator uses the height formula:

\[ h = \sqrt{leg^2 - \left(\frac{base}{2}\right)^2} \]

Where:

\( h \) — Height of the triangle
\( leg \) — Length of the equal sides
\( base \) — Length of the base side

Explanation: The formula is derived from the Pythagorean theorem, applied to one of the two right triangles formed by the height.

3. Importance of Height Calculation

Details: Knowing the height is essential for calculating area, determining triangle properties, and solving geometry problems involving isosceles triangles.

4. Using the Calculator

Tips: Enter the lengths of the equal sides (legs) and the base. All values must be positive numbers. The calculator will compute the height.

5. Frequently Asked Questions (FAQ)

Q1: What is an isosceles triangle?
A: An isosceles triangle is a triangle with at least two sides of equal length.

Q2: Can this formula be used for all triangles?
A: No, this specific formula only works for isosceles triangles. Other triangle types require different height calculations.

Q3: What units should I use?
A: Use consistent units for all measurements (e.g., all in cm or all in inches). The result will be in the same units.

Q4: What if my base is longer than twice the leg length?
A: The input would be invalid as it would violate the triangle inequality theorem (leg + leg > base).

Q5: How is this different from the area formula?
A: The area is (base × height)/2. This calculator finds the height which can then be used to calculate area if needed.