INTRODUCTION:                      

Triangle is a polygon with three sides. Triangle is formed by connecting the three non-collinear points using straight line segments.  It is a closed shape that consists of three line segments that are linked end to end. It has three edges and three vertices. The total interior angle of triangle is 180 degrees. Based on sides and angles, the triangles are classified in to the following types: Right angled, Equilateral and Isosceles triangle.

 

 

Formula for Height of a Triangle

 

There are two methods by which we can find the height of the triangle.

  • Pythagorean Theorem.
  • Area of the triangle formula.

 

Pythagorean Theorem formula:

Pythagorean Theorem says that the sum of the squares of the two sides of a right triangle is equal to the square of the hypotenuse.

(Height)2 + (base)2 = (Hypotenuse)2

(Height)= (Hypotenuse)2 - (base)2

Area of Triangle formula:

Area = (1/2) * Base * Height

To find height of a triangle;   Height = (Area) / ((1/2) * Base)

 

Examples:

 

1. Find the height of a triangle with a base of 6 inches and hypotenuse of 8 inches.

solution:

To find the height of a given triangle use the following formula,

(Height)2   =  (Hypotenuse)2  -  (base)2

Step 1:  (Height)2   = (8)2   -   (6)2

Step 2:  (Height)2   = 64     -   36

Step 3: (Height)2   =   28

Take the square root both sides.

Step 4:  Height    = 5.29

Hence the answer is 5.29 inches. 

 

2. Find the height of a triangle with base 4 cm and area 28 sq cm.

Solution:

To find the height of a given triangle use the following formula,

Formula:  Height     =   (Area) / ((1/2) * Base)

Step 1:  Height     =   (28) / ((0.5) * 4)

Step 2:  Height     =    28 / 2

Step 3:  Height     =    14 centimeter.

Hence the answer is 14 centimeter.

 

3. Find the height of a triangle with base 6 centimeter and area 14 square centimeters.

Solution:

To find the height of a given triangle use the following formula,

Height     =   (Area) / ((1/2) * Base)

Step 1:  Height     =   (14) / ((0.5) * 6)

Step 2:  Height     =    14 / 3

Step 3:  Height     =    4.67 centimeter.

Hence the answer is 4.67 centimeter.