The first step is to find the reference angle then label our opposite,adjacent,hypotenuse
then decide which trig function to use and then set it up.
The first part I'm going to show you just how to do these four steps then on the second
page we will go through and solve them.
Let's look at this set up.
We want to use this 52 degree angle as our reference angle.
So from this 52 degree angle this side is the opposite this side is the hypotenuse,and
this side is the adjacent.
Which two sides are we using.
Their is not any marking on the hypotenuse,so we will use the opposite side and the adjacent
side.
Look at your reference and which trig ratio (I'll jot them up here opposite hypotenuse,adjacent
hypotenuse, and opposite,adjacent) Which one uses opposite side over the adjacent.
Well that is our tangent.
So that is how we decide which trig function to use.
So let's set up the tangent of theta which is our reference angle.
We take the tangent of 52 degrees and that is equal to the opposite side over the adjacent
side so now we will write a ratio opposite is x and adjacent is 12 and that is how we
set it up.
So there is our first part.
So let's go down and practice setting these first three problems up.
Not solving them yet,just setting them up.
So I will jot this down for later I have a tangent of 52 is equal to 12 over x Now let's
look at this practice problem.
Here is our right triangle we have a 48 degree angle here so that is our reference angle,we
have 17 on this side and x on this side.
So from this reference angle which two sides are we dealing with.
So from here this side x is the opposite and and the side marked 17 is the hypotenuse so
we have sin,cosine, I will jot them down again, and which trig function uses the opposite
over hypotenuse.
That is the sine function because it opposite and hypotenuse.
I will set up the sine of what angle?
My reference angle is 48 degrees and that is equal to opposite over hypotenuse.
My opposite is the unknown and it is on top and my hypotenuse is 17 so the first problem
is sin of 48 is equal to x over 17.
Let's try the third problem.
The second practice problem.
We have a 72 degree reference angle we have 34 over here x over here.
From the 72 degree angle x is our opposite and this is our hypotenuse and this one is
our adjacent.
We are not using hypotenuse so which trig function uses adjacent and opposite?
Tangent uses opposite and adjacent.
We will set up the tangent of 72 is equal to the ratio of which two sides?
Opposite over adjacent so I will have x over 34 so this one sets up as the tangent of 72
is equal to x over 34