Calculator Form
Example Data Table
| Method | Known Inputs | Apex Angle | Each Base Angle | Notes |
|---|---|---|---|---|
| Apex angle | 40° | 40° | 70° | Direct angle relation |
| Base angle | 50° | 80° | 50° | Uses A = 180 - 2B |
| Equal and base sides | s = 10, c = 12 | 73.74° | 53.13° | Law of cosines |
| Height and base side | h = 8, c = 12 | 73.74° | 53.13° | Right triangle split |
| Area and base side | K = 48, c = 12 | 73.74° | 53.13° | Area first gives height |
Formula Used
For an isosceles triangle, the two base angles are equal.
1. Interior angle rule: apex angle + 2 × base angle = 180°
2. From apex angle A: base angle = (180° - A) / 2
3. From base angle B: apex angle = 180° - 2B
4. From equal side s and base side c: apex angle = arccos((2s² - c²) / (2s²))
5. Height formula: h = √(s² - (c/2)²)
6. From height h and base c: apex angle = 2 × arctan((c/2) / h)
7. From area K and base c: h = 2K / c, then use the height formula above.
How to Use This Calculator
- Select the input method that matches your known triangle data.
- Enter the required value or values in the visible fields.
- Choose the number of decimal places for the output.
- Press Calculate to display the solved triangle above the form.
- Review the angles, derived dimensions, and step-by-step calculation.
- Use the CSV or PDF buttons to save the current result.
- Check the Plotly graph to inspect the solved triangle visually.
FAQs
1. What makes a triangle isosceles?
An isosceles triangle has two equal sides. Because of that symmetry, the two base angles are also equal. This calculator uses that rule in every method.
2. Can I solve the triangle from one angle only?
Yes. If you know the apex angle or one base angle, the other angles follow directly from the 180° interior angle sum.
3. Why are side values normalized for angle-only inputs?
Angles alone do not fix an absolute size. The calculator scales the equal side to 1 unit so it can still draw the triangle and estimate relative dimensions.
4. What if my base side is too large?
If the base side is at least twice the equal side, no valid isosceles triangle exists. The calculator checks that before solving.
5. Can I use area to get the angles?
Yes. When area and base are known, the calculator first finds height. Then it uses the split right triangle to determine the apex and base angles.
6. Why does the calculator show radians too?
Radians are useful in higher mathematics, trigonometry, and programming. Showing both degree and radian values makes the output more practical.
7. What does the Plotly graph represent?
It plots the solved triangle using your measured sides or a normalized scale. The labels help you inspect the apex and base angles visually.
8. Can I download the result for reports?
Yes. The page includes CSV export for tabular use and PDF export for clean sharing, printing, or record keeping.