# How and when do we use SOHCAHTOA?

May 19, 2016

Below are a few examples I have prepared.

#### Explanation:

Multiplication:

Example:

First, we have to find what positions side a and the side measuring 37 cm are relative to the given angle, which is 43˚.

•a is opposite

• 37 cm is the hypotenuse

By SOHCAHTOA, an opposite and a hypotenuse gives $\sin$.

Now, we write our proportion.

$\frac{a}{37} = \sin \frac{43}{1}$

Now, we must solve for a. This can be done by using the property $\frac{a}{b} = \frac{n}{m} \to a \times m = b \times n$

$a \times 1 = 37 \left(\sin 43\right)$

$a = 37 \sin 43$

Calculating, we get that a measures 25.23 cm.

The trick to the multiplication: always make a proportion.

Division:

Consider the following example:

Once again, from 21˚, identifying the sides we know, we find that we know adjacent and hypotenuse. Looking through SOHCAHTOA, we find that adjacent/hypotenuse is represented by $\cos$.

Writing our proportion:

16/x = (cos21˚)/1

Here, we have a division. Same thing as last time however; we use the property $\frac{a}{b} = \frac{m}{n} \to a \times n = b \times m$

x = 16/(cos21˚)

$x = 17.14 c m$

The best trick:

If you are solving for the hypotenuse, and the ratio you are using is sin or cos, then it will be a division (the side you are solving for is on the bottom ). If you are solving for one of the legs, it will be a multiplication. However, tangent depends on the case (it can be either way). As I said many times before, most importantly, set up your proportion and use the property $\frac{a}{b} = \frac{m}{n} \to a \times n = b \times m$: This is key to your success in this unit.

Feel free to send me a message if you need any additional help.

Hopefully you understand better now.