SOHCAHTOA AND ITS APPLICATION IN TRIGONOMETRY

What is SOHCAHTOA ? 

In Trigonometric term SOHCAHTOA can be defined by the explaining the trigonometric ratios:

• SOH (Sin(θ))= Opposite/Hypotenuse
• CAH (Cos(θ)) = Adjacent/Hypotenuse
• TOA (Tan(θ))= Opposite/Adjacent

Now just remember the word “SOH CAH TOA”, it can be quite easy to find the values of all the trigonometric ratios like Sin is Opposite/Hypotenuse, so we are going to write it as “SOH”. The Cos is  Adjacent/Hypotenuse, we are going to write it as “CAH “, and  TOA stands for tan is equal to opposite over hypotenuse.

When you are using the  trigonometry calculator, then you can convert one form of trigonometry into another readily. When you are able to remember all word SOHCAHTOA, then you can remember all the trigonometric ratio in one word

What are the three sides of a right angle triangle?

In a right angle triangle, there are 3 sides, the Hypotenuse, Opposite side and Adjacent. You may also say the opposite side is the perpendicular, and the  Adjacent side is the base of the triangle.  For the sohcahtoa calculator, we are using the terms  Hypotenuse, Opposite side and Adjacent side.

Opposite side:

Opposite side is the opposite to the angle of the triangle, in the triangle ABC, the “BC” is the opposite side.

Adjacent side:

It is side along with the angle, and residing horizontally to the side of the triangle. In this case the side “AB” is the adjacent side of the triangle.

Hypotenuse:

Hypotenuse is the side which is making an angle with the adjacent side. The Hypotenuse is normally the longest side of the right angle triangle.

When you are using the sohcahtoa calculator, you need to understand, just enter the values of the missing side and enter the angle of your triangle.

Example 1 of SOHCAHTOA :

Consider a right angle triangle ABC, where BC = 10 cm, and angle A = 20 degrees, then find side CA.

Solution:

angle A = 20 degrees

BC = 10 cm and CA = ?

Here, you know we have an angle and length of the side, We can apply the sine ratio to find the answer.

Now by SOHCAHTOA formula, we know that:

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

You can use the sohcahtoa calculator to find the length of the side “CA”. Sometimes, there are two sides are given and you need to find an angle between them.

Example 2 of SOHCAHTOA:

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

Solution :

BC = 10 cm, CA = 20 and  θ = ?

Here, you know we have an angle and length of the side, We can apply the Sine ratio to find the answer.

Now by SOHCAHTOA formula, we know that:

sin θ =  Opposite/Hypotenuse

sin θ = BC/CA 

As BC = Opposite  CA = Hypotenuse

Then:

sin  θ = 10/20

sin θ = 10/20

sin θ = 1/2

θ = sin^-1(1/2)

θ = 30