Calculator Inputs
Choose a method, enter values, and calculate the triangle height with graph-ready output.
Example Data Table
These examples show how each method can be used to compute triangle height.
| Method | Input Values | Calculated Height | Notes |
|---|---|---|---|
| Area and Base | Area = 24, Base = 8 | 6 | Uses h = 2A / b. |
| Three Sides | Base = 10, Left = 13, Right = 13 | 12 | Heron’s formula gives the area first. |
| Coordinates | A(0,0), B(8,0), C(3,6) | 6 | Height is the perpendicular distance to AB. |
| Base, Side, and Included Angle | Base = 9, Side = 7, Angle = 60° | 6.0621778265 | Uses h = side × sin(angle). |
Formula Used
1) Area and Base
Height = (2 × Area) ÷ Base
2) Three Sides
s = (a + b + c) ÷ 2
Area = √[s(s-a)(s-b)(s-c)]
Height to chosen base = (2 × Area) ÷ Base
3) Coordinates
Base AB = √[(x₂-x₁)² + (y₂-y₁)²]
Double Area = |(B-A) × (C-A)|
Height to AB = Double Area ÷ Base AB
4) Base, Side, and Included Angle
Height = Adjacent Side × sin(θ)
How to Use This Calculator
- Select the input method that matches your available data.
- Enter all required values in the visible fields.
- Press Calculate Height to compute the result.
- Review the result box above the form for height, area, perimeter, and coordinates.
- Inspect the plotted triangle and altitude in the graph section.
- Use the CSV or PDF buttons to export the displayed report.
Frequently Asked Questions
1) What does the triangle height represent?
Triangle height is the perpendicular distance from a chosen vertex to the opposite side, or that side’s extension. It is also called altitude.
2) Which base does this calculator use?
The calculator uses the base implied by your chosen method. For coordinates, the base is segment AB. For three sides, the entered base side is used.
3) Why does the graph sometimes look isosceles?
In area-and-base mode, the graph uses an illustrative isosceles shape to visualize the computed height. The numeric height remains correct for the entered values.
4) Can I use decimal values?
Yes. The calculator accepts decimal values for lengths, coordinates, area, and angles. Results are shown with up to ten decimal places.
5) What happens if the sides cannot form a triangle?
The calculator checks triangle inequality in the three-sides method. If the values are invalid, it shows an error instead of a misleading result.
6) Why is the coordinate method useful?
It is useful when geometry is plotted on axes. You can calculate the exact perpendicular height from point C to line AB directly from coordinates.
7) Does the PDF include the graph?
The PDF export focuses on the result summary and the example table for a clean report. The live graph remains available on the webpage.
8) Is this calculator suitable for homework and planning?
Yes. It works well for classroom checks, geometry practice, engineering sketches, and quick triangle height verification with multiple input styles.