Introduction:

There are three sides in a triangle. The height of the triangle can be calculated in different ways. It is all depends on the information provided in the question. Height is the measurement of vertical distance. Perpendicular distance from a vertex to the opposite side of a triangle is called height.

Height of the triangle can be calculated according to information provided :

**For Right angle triangle:**

Using Pythagorean theorem: According to this theorem square of hypotenuse is equal to the sum of squares of its two sides.

Let the sides are B and P and Hypotenuse H

here P is the height of the triangle

then according to Pythagorean theorem

H^{2} = B^{2} + P^{2}

P^{2} = H^{2} - B^{2}

(height of the triangle)^{2} = (Hypotenuse)^{2} - (Base)^{2}

This way we find the square of height.

Now take the square root.

(height of the triangle) = √ Hypotenuse^{2} - Base^{2}

Example:

Find the height of the given figure?

This is a right angle triangle.

here b = 3, H = 5

height of the triangle= √ Hypotenuse^{2} - Base^{2}

h = √ 5^{2} - 3^{2}

h = √ 16 h = 4 unit

Following formula is used.

Area of the triangle = 1/2 x base x height

height = (2 x Area of the triangle )/ base

Example:

Calculate the height of the triangle if the area is 150 cm^{2} and base is 12cm.

using the formula

Area of the triangle = 1/2 x base x height

150 = 1/2 x 12 x h

150 = 6x h

`rArr` 150/6 = h

25 = h

h = 25 cm.

For different base , corresponding height is different. In above example , height h is corresponding to base 12.

Equilateral triangles are the triangles having all sides of same length.

height of an equilateral triangle = `sqrt(3)` / 2 x side