Triangle Height Calculator

Enter known triangle values and choose a method. See height, area, checks, units, and conversions. Use clear outputs for study, design, and lesson planning.

Enter Triangle Values

Example Data Table

Method Inputs Formula Expected Height
Area and base Area = 48, Base = 12 h = 2A ÷ b 8
Three sides a = 13, b = 14, c = 15, base = c Heron, then h = 2A ÷ c 11.2
Trigonometry Side = 8, Angle = 60° h = side × sin(angle) 6.9282
Equilateral Side = 10 h = √3 ÷ 2 × side 8.6603
Coordinates A(0,0), B(10,0), C(5,8) h = cross product ÷ base 8

Formula Used

Area and base: h = 2A ÷ b. Use this when area and matching base are known.

Three sides: s = (a+b+c)/2. Then A = √[s(s-a)(s-b)(s-c)]. Finally, h = 2A ÷ selected base.

Slanted side and angle: h = slanted side × sin(angle). The angle must touch the base and the slanted side.

Equilateral triangle: h = (√3 ÷ 2) × side. This works only when all three sides are equal.

Coordinates: h = |(B-A) × (C-A)| ÷ |B-A|. The base is the segment from A to B.

How to Use This Calculator

  1. Select the method that matches your known values.
  2. Enter all required numbers in the visible fields.
  3. Choose the unit and decimal places.
  4. Press the calculate button.
  5. Read the result block above the form.
  6. Download CSV or PDF if you need a saved report.

Understanding Triangle Height

Triangle height is the perpendicular distance from a chosen base to the opposite vertex. It is not always the visible side of the triangle. In a right triangle, one leg may be the height. In an obtuse triangle, the height can fall outside the shape. That is why a flexible calculator is helpful.

Why Height Matters

Height connects many triangle measurements. Area needs a base and its matching height. Structural sketches use height to check clearance. School problems use height to compare formulas. Surveying and design tasks use it to convert sloped lengths into vertical distances. A wrong base choice gives a wrong height, even when the numbers look reasonable.

Choosing the Best Method

Use area and base when both are known. This is the fastest method. Use three sides when only side lengths are available. The calculator first applies Heron's formula, then divides twice the area by the selected base. Use the trigonometry option when a slanted side and its angle with the base are known. Use coordinates when each vertex is placed on a grid. Use the equilateral option when all sides are equal.

Checking Your Result

A good result should match the triangle shape. The height must be positive. For most drawn triangles, it is smaller than a long slanted side. The side method must pass the triangle inequality rule. Coordinate points must not place the base endpoints at the same location. When values fail these checks, the page explains the issue before showing a final answer.

Practical Use

The result card gives height, base, area, and extra notes. The chart shows a quick visual model, so you can inspect the base and altitude. CSV export helps with spreadsheets. PDF export is useful for homework records, project notes, and shared reports. The example table shows common inputs. Together, these tools make the calculator useful for study, teaching, drafting, landscaping, construction planning, and general geometry work.

Common Input Tips

Keep units consistent across every field. Do not mix inches, meters, and feet. Round outputs only after calculation. Enter angles carefully. Degrees are common in classwork. Radians are common in technical work and advanced software tools.

FAQs

1. What is the height of a triangle?

The height is the perpendicular distance from a selected base to the opposite vertex. It must meet the base or its extended line at a right angle.

2. Can any side be used as the base?

Yes. Any side can be the base, but the height must match that chosen side. Changing the base usually changes the height.

3. How do I find height from area?

Use h = 2A ÷ b. Multiply the area by two, then divide by the matching base length.

4. How does the three side method work?

It uses Heron's formula to find area from three sides. Then it divides twice that area by the selected base.

5. What angle should I enter for trigonometry?

Enter the angle between the base and the slanted side. The calculator uses the sine of that angle to find vertical height.

6. Why can height fall outside a triangle?

In an obtuse triangle, the perpendicular altitude may meet an extension of the base. The height is still valid because it is perpendicular.

7. Can coordinates give triangle height?

Yes. The coordinate method uses the distance from point C to the line through points A and B.

8. Why is my result not shown?

The inputs may be incomplete, negative, impossible, or collinear. Read the error message and correct the highlighted values.

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Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.