Triangle Calculator – Your Tool to Solve Any Triangle Easily

Our Triangle Calculator is a powerful online tool designed to help you quickly and accurately calculate all important properties of a triangle when you know its three sides. Whether you’re a student, teacher, engineer, or simply curious, this tool makes solving triangle problems simple and intuitive.

What can the Triangle Calculator do?

• Calculate the perimeter and area using Heron’s formula.

• Determine all three internal angles using the Law of Cosines.

• Compute the heights (altitudes) relative to each side.

• Display a precise scaled drawing of the triangle for visualization.

• Provide additional triangle properties such as inradius, circumradius, and medians (optional).

How does the Triangle Calculator work?

When you enter the lengths of the three sides $a$ , $b$ , and $c$ , the calculator performs the following steps:

1. Validity check: Ensures the sides satisfy the triangle inequality so a valid triangle can exist.

2. Calculate perimeter: Simply sums up the three sides.

3. Calculate semiperimeter: Half the perimeter, used in further formulas.

4. Calculate area: Uses Heron’s formula, which computes area solely from the side lengths without needing angles.

5. Calculate angles: Applies the Law of Cosines to find each internal angle accurately.

6. Calculate heights: Computes altitudes from each vertex to the opposite side using the area.

7. Draw the triangle: Uses coordinate geometry to plot the triangle to scale on a canvas.

8. (Optional) Calculate other properties: Such as the inradius (radius of the inscribed circle), circumradius (radius of the circumscribed circle), and lengths of medians.

Example Calculation with Sides a=5, b=5, c=7

• Perimeter
  $p = 5 + 5 + 7 = 17$ 

• Semiperimeter
  $s = 17 / 2 = 8.5$ 

• Area
  $T = \sqrt{8.5 \times (8.5-5) \times (8.5-5) \times (8.5-7)} \approx 12.497$ 

• Heights
  $h_a = \frac{2 \times 12.497}{5} = 4.999$ 

• Angles approximately:
  $45^\circ 34′ 23”$45∘34′23′′, $45^\circ 34′ 23”$, and ${88}^{\circ }{51}^{\mathrm{\prime }}{14}^{\mathrm{}}$