# Mastering Trigonometry with SOHCAHTOA: Theory and Applications

Tuesday, March 21, 2023

The “SOHCAHTOA” is a word and mnemonic for remembering trigonometric ratios. Here the SOH stands for the Sin is equal to the Opposite over the Hypotenuse.

The CAH for the cos equals the Adjacent over the Hypotenuse, and TOA is the Tan of Opposite over the Adjacent.

The Sohcahtoa Calculator identifies the trigonometric ratios and answers the missing sides and the angles. When you can remember the “SOHCAHTOA.”

Then it is possible to remember all the trigonometric ratios as you can also not forget the Cosec, Sec, and Cot ratios as these are opposite to the Sin, Cos, and Tan.

## What is the Sohcahtoa mnemonic?

The Sohcahtoa mnemonic can remember all six trigonometric ratios, and all are re

• SOH (Sin(θ))= Opposite/Hypotenuse

When you can remember these three ratios, it is possible to learn the Opposite of the Sin, Cos, and Tan, which are Cosec θ, Sec θ, and  Cot θ.

Cosec θ = Sin-1θ = Hypotenuse/ Opposite

Sec θ  = Cos-1θ =  Hypotenuse/Adjacent

Cot θ = Tan-1 θ =   Adjacent/Opposite

The adjacent side of the triangle is the side along the angle of the right-angle triangle. In the figure above, the AB is the adjacent side of the triangle.

## Opposite side:

The opposite side of the triangle is the side opposite the angle of the right-angle triangle. In the figure above, the BC is on the opposite side of the triangle.

## Hypotenuse:

The Hypotenuse of the triangle is the side along the angle of the right-angle triangle. In the figure above, the AC is the Hypotenuse of the triangle.

Use the trigonometry calculator to find the adjacent side, the Opposite side, and the Hypotenuse of a right-angle triangle.

## SOHCAHTOA Example 1:

A right angle triangle ABC, the BC = 10 cm, and angle A = 20, then determine the side CA.

Solution:

Here A = 20 degrees

BC = 10 cm

CA =?

Sin θ =  Opposite/Hypotenuse

Sin θ = BC/CA

As BC = Opposite

And CA = Hypotenuse

Then:

Sin 20 = 10/CA

Sin 20/10 = 1/CA

CA =  10/Sin 20

CA =  29.24 cm

The Sohcahtoa Calculator can be used to find the missing side and the angles.

### SOHCAHTOA Example 2:

A right angle triangle ABC, where BC = 10 cm, CA= 20 cm, and determine the angle A.

Solution:

BC = 10 cm

CA= 20

θ = ?

Sin θ =  Opposite/Hypotenuse

Sin θ = BC/CA

As BC = Opposite

And CA = Hypotenuse

Then:

Sin  θ = 10/20

Sin  θ= 10/20

Sin  θ = 1/2

θ =Sin-1(½)

θ = 30

## Conclusion:

The  Sohcahtoa Calculator can be used to find the missing side and the angles of the right angles of the triangle. When you can learn what is the meaning of the Sohcahtoa.

Then it would become easy for you to know the trigonometric ratios, and you can understand them. Trigonometry is one of the essential branches of geometry.