# How and when do we use SOHCAHTOA?

##### 1 Answer

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

By SOHCAHTOA, an opposite and a hypotenuse gives

Now, we write our proportion.

Now, we must solve for a. This can be done by using the property

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

Writing our proportion:

Here, we have a division. Same thing as last time however; we use the property

**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 #a/b = m/n -> a xx n = b xx 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.