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Triangle Calculator Without Height

Reviewed by Calculator Editorial Team

This triangle calculator helps you find missing sides, angles, and area of a triangle when you don't have the height. Whether you're solving for a right triangle or using the Law of Cosines/Sines, this tool provides accurate results with clear explanations.

How to Use This Calculator

To use this triangle calculator without height, follow these simple steps:

  1. Select the type of triangle you're working with (right triangle or general triangle).
  2. For right triangles, enter the two known sides (adjacent and opposite).
  3. For general triangles, enter the three sides or two sides and the included angle.
  4. Click "Calculate" to see the results.
  5. Review the calculated values and the triangle visualization.

The calculator will determine the missing sides, angles, and area based on your inputs. All calculations are performed using precise mathematical formulas.

Formulas Used

This calculator uses different formulas depending on the type of triangle and the information you provide:

Right Triangle Formulas

For right triangles, we use the Pythagorean theorem and trigonometric functions:

  • Pythagorean theorem: c² = a² + b²
  • Sine of angle A: sin(A) = opposite/hypotenuse
  • Cosine of angle A: cos(A) = adjacent/hypotenuse
  • Area: Area = (base × height) / 2

General Triangle Formulas

For non-right triangles, we use the Law of Cosines and Law of Sines:

  • Law of Cosines: c² = a² + b² - 2ab cos(C)
  • Law of Sines: a/sin(A) = b/sin(B) = c/sin(C)
  • Area using two sides and included angle: Area = (ab sin(C)) / 2
  • Area using Heron's formula: Area = √[s(s-a)(s-b)(s-c)] where s = (a+b+c)/2

All calculations are performed with JavaScript in your browser, ensuring your data stays private and secure.

Worked Examples

Let's look at some practical examples of how to use this calculator:

Example 1: Right Triangle

Given a right triangle with sides a = 3 and b = 4, what are the other sides and angles?

  1. Select "Right Triangle" from the triangle type dropdown.
  2. Enter 3 for side a and 4 for side b.
  3. Click "Calculate".
  4. The calculator will show:
    • Side c (hypotenuse) = 5
    • Angle A = 53.13°
    • Angle B = 36.87°
    • Area = 6

Example 2: General Triangle

Given a triangle with sides a = 5, b = 7, and angle C = 45°, what are the other sides and angles?

  1. Select "General Triangle" from the triangle type dropdown.
  2. Enter 5 for side a, 7 for side b, and 45 for angle C.
  3. Click "Calculate".
  4. The calculator will show:
    • Side c ≈ 6.32
    • Angle A ≈ 53.13°
    • Angle B ≈ 81.87°
    • Area ≈ 13.97

Frequently Asked Questions

Can I use this calculator for any type of triangle?
Yes, this calculator works for both right triangles and general triangles. Simply select the appropriate triangle type and provide the known values.
What if I don't know any angles?
For right triangles, the angles are always 90°, 45°, and 45°. For general triangles, you need to know at least one angle or have enough side information to determine the angles using the Law of Sines or Cosines.
Is the height calculation included?
No, this calculator specifically helps you find triangle properties without needing the height as an input. The height is calculated when possible based on the other triangle properties.
How accurate are the calculations?
The calculations are performed using standard mathematical formulas with JavaScript's built-in precision. Results are typically accurate to at least 4 decimal places.