Right Triangles?

Question

I have been working with finding sides (given one side and an angle) in Right triangles and have improved greatly with determine the trig function to use.

My question is how do I determine if I multiply to get an answer, ex: 7tan(45) or divide, ex:4/sin(35)

What information is being provided that determine whether I multiply or divide to arrive at a final answer?

Thank you,

Brian

Answer 1

Whether you multiply or divide is based on your equation. Will show you an example using tan.

tan = opposite/adjacent

Let's say you are solving for the opposite side.

tan 40 = x/2

To solve for x, you have to multiply both sides of the equation by 2 to get rid of the fraction

2(tan 40) = (x/2)(2)

See on the right side how the 2s cancel out? You are left with

2(tan 40) = x (Multiplication scenario you talked about)

Now you are solving for the adjacent side this time

tan 40 = 3/x

This time to get ride of the fraction, you have to multiply both sides of the equation by x

x(tan 40) = (3/x)(x)

What has happened on the right side this time? The xs cancel out. You are left with

x(tan 40) = 3

We have gotten rid of the fractions, but we still don't have x by itself. We still don't have x by itself. To get x by itself, you have to divide both sides of the equation by tan 40

x(tan 40)/(tan 40) = 3/(tan 40)

Focusing on the left side now, see how tan 40/tan 40 cancels out? You are left with

x = 3/(tan 40) (This is the division case)

You will find that it is best to not try to memorize when to multiply versus dividing. If you focus on how to solve for x, you will be right every time.