Triangle Height Calculator

What Is FREE TOOLS Triangle Height Calculator?

A Triangle Height Calculator is a free online tool used to calculate the height (altitude) of a triangle from its known measurements.

The height of a triangle is the perpendicular distance from a vertex to the opposite side, or to the extension of that side.

Triangle Height Formula

The most common formula comes from the triangle area formula: A=12bhA=\frac{1}{2}bh

Rearranging it to find height: h=2Ab\boxed{h=\frac{2A}{b}}

Where:

h = triangle height
A = triangle area
b = base

Example

Suppose a triangle has:

Area = 40 square units
Base = 10 units

Then: h=2(40)10h=\frac{2(40)}{10} h=8h=8

Therefore, the triangle’s height is 8 units.

Finding Height From Three Sides

If all three side lengths are known, the calculator can first find the area using Heron’s Formula: s=a+b+c2s=\frac{a+b+c}{2} A=s(s−a)(s−b)(s−c)A=\sqrt{s(s-a)(s-b)(s-c)}

Then the height can be calculated using: h=2Ab\boxed{h=\frac{2A}{b}}

For example, if the sides are 5, 6, and 7, the area is approximately: A≈14.697A\approx14.697

Using the side of 6 as the base: h=2(14.697)6h=\frac{2(14.697)}{6} h≈4.899h\approx4.899

So the height relative to the 6-unit base is approximately 4.90 units.

Height of an Equilateral Triangle

For an equilateral triangle with side length ss, the height is: h=32s\boxed{h=\frac{\sqrt{3}}{2}s}

For example, if each side is 10 units: h=32(10)h=\frac{\sqrt{3}}{2}(10) h≈8.66h\approx8.66

The height is approximately 8.66 units.

How Does a Triangle Height Calculator Work?

A FREE TOOLS Triangle Height Calculator can use different combinations of known measurements, including:

Area and base
Three side lengths
Base and other triangle measurements
Side length for an equilateral triangle
Angles and sides using trigonometry

The calculator determines the appropriate formula and returns the corresponding altitude.

Why Use a Triangle Height Calculator?

It can be useful for:

Geometry homework
Trigonometry problems
Construction
Architecture
Engineering
Surveying
Land measurement
Design calculations
Checking manual calculations

Important Note

A triangle can have three different heights, because each side can be selected as the base. The height changes depending on which side is being used as the base.

For the formula: h=2Abh=\frac{2A}{b}

the height calculated is specifically the perpendicular height corresponding to base bb.

In Simple Terms

A FREE TOOLS Triangle Height Calculator quickly finds the perpendicular altitude of a triangle when enough information is available.

The primary formula is: h=2Ab\boxed{h=\frac{2A}{b}}

It is a useful tool for calculating triangle heights without having to perform lengthy geometry or trigonometry calculations manually.

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FREE TOOLS Triangle Height Calculator