How To Apply SOHCAHTOA In Right Angle Triangles

When solving mathematical problems, the technical know-how and the understanding of basic principles is all that is need.  This also applies to every part of mathematics including SOHCAHTOA which is the abbreviated form of Sine, Cosine, And Tangent. Understanding it might be demanding, but with the right information and explanation, the application process is quite easy.

Having had issues with this particular topic over the years until I was able to understand what it is all about, I know how frustrating and confusing this can be to mathematics students. With the hopes of preventing others from going through what I went through, I have prepared a quick but detailed lesson to help guide and improve the knowledge base of students who are interested in understanding how SOHCAHTOA works. 

First of all, let’s understand what SOHCAHTOA is all about before taking a look at how to apply sine, cosine, and tangent in right angle triangles to find either one or two missing lengths. 


According to what I was able to learn, SOHCAHTOA is a just a simple abbreviation of sine, cosine, and tangent of a right-angle triangle. Each of these abbreviated words has their respective formulas which can be used to solve for a missing angle or sides.  

A perfect right angle triangle has three major sides which are the opposite, adjacent, and hypotenuse. Before I was able to apply the formula of SOHCAHTOA, I needed to understand that opposite of these three in a right-angle triangle. After figuring that out, then I was able to apply this formula easily. 

From my studies, I was able to understand to that the longest part of a right angle triangle is the Hypotenuse, while the side opposite the selected angle is the opposite side, and lastly, the adjacent side is the side which is beside the selected angle. 

How to apply SOHCAHTOA to find the sides of a right-angle triangle 

The above explanation of what SOHCAHTOA all about serves as the rudiment for calculating either angles or missing sides of a right-angle triangle. With the knowledge I was able to acquire, understanding the formula was quite easy. 

By separating the formula, it splits into SOH CAH TOA, each standing as a separate entity. The SOH here represents  sin\theta and the formula is opposite\hypotenuse. While CAH represents cos\theta and the formula is adjacent\hypotenuse. Lastly, TOA represents tan\theta and it has a general formula which is opposite\adjacent. 

Let’s take a look at an example to help enhance the understanding of what SOHCAHTOA is. Let’s say we have a right angle triangle with an opposite angle of 30 degrees and an opposite side of 4cm. From our previous knowledge, sin\theta = opposite\hypotenuse which is SOH is the best formula to solve this problem. 

By substituting the variables in the formula, the equation changes to sin 30= 4\hypotenuse. From here, we will have 0.5=4\x (x= hypotenuse) and finally, by multiplying x on both sides, our final answer becomes 4.


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About the Author: Donald Phillips