\[h=\sqrt{a^2-\left(\frac{b}{2}\right)^2}\]
Variables
htriangle height (m)
aequal side length (m)
bbase length (m)
Description
What is this formula?
This formula calculates the height of an isosceles triangle using the lengths of its equal sides and base.
In an isosceles triangle, the altitude from the top vertex divides the base into two equal segments, creating two right triangles.
The formula is derived from the Pythagorean theorem.
When to use it
Use this formula when:
- The triangle is isosceles
- The equal side lengths are known
- The base length is known
- The height must be determined
- Solving geometry or construction problems
This method avoids the need for angle measurements.
Example
If:
a = 10 m
b = 12 m
Then:
h = √(10²-(12/2)²)
h = √(100-36)
h = √64
h = 8 m
Applications
- Geometry and trigonometry
- Structural engineering
- Architecture and design
- Construction calculations
- CAD modeling
- Educational mathematics