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How To Find The Height Of An Oblique Triangle?

A triangle is a geometrical shape which has three line segments equal or different in size joined with each other at a different or same angle. Main components which a triangle consists are 3 sides and 3 angles associated with them.

Depending on the different sizes of its elements it is classified into 3 different types but here we will only discuss oblique triangle. As we have studied in high school, calculating the height of a 90 degrees triangle is quite easy and we have Pythagorean Theorem if all sides are known.

Calculating the height of an oblique triangle is difficult but in this article, we will try to solve it step by step for better understanding so keep reading the article until the end.

Oblique Triangle

an oblique triangle

For those who are not familiar with oblique triangle here is a brief introduction. An oblique triangle is that which has no right angle or 90-degree angle. It can either have three acute angles or two acute and one imperceptive angle. It is important to note that sum of angles of any triangle would be 180-degree.

Calculating the Height

example of triangle

Let’s take an example of an oblique triangle as shown in figure. Here P, Q, R are the angles, p, q, r are the sides.

There are two different ways to calculate height

Calculating height using Law of sine

According to law of sine

Sine = perpendicular / hypotenuse

Step 1

law of sine step 1

First of all, we consider a right angle triangle by sketching a straight line h which is the height of an oblique triangle.

Step 2

law of sine step 2

Measure the length of hypotenuse using a scale let’s say it is 7 cm and angle using protector suppose it is 30 degree.

Step 3

As we have perpendicular as h and hypotenuse as q so we can write

Sine = h/q

We have to calculate h so we can write formula as

h = q* sin ()

Step 4

Put the values

h = 7 * sin(30)

h = 7 * 0.5

h= 3.5 cm

So the height of this oblique triangle is 3.5 cm.

Calculating height using Area

height using area

Let’s take an example of an oblique triangle whose area is given to you which is 5 cm2 and its base is 7 cm.

According to the formula of area

Area = ½ *base * height

Step 1

We have to find height so write the formula as

Height = 2* area/base


h = 2* Area/r

Step 2

Put the values and calculate

h = 2 * 5/7

h= 5.3 cm

So from above examples, we learned the ways to calculate the height of an oblique triangle. I hope it was easy to understand for you and if you have questions you can write it down in the comments section.


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