TANGENT – FIND THE SIDE
OBJECTIVE
Now, for the last time, let’s go back to �SOHCAHTOA
SOHCAHTOA
A really weird acronym that will help you remember the basic trig functions
Let’s break them down:
S – Sine
O- Opposite
H- Hypotenuse
C- Cosine
A- Adjacent
H – Hypotenuse
T- Tangent
O- Opposite
A- Adjacent
So, what does this all mean?
It means this:
One last look at the sides.
Basically what we mean is when looking at a triangle, the angle that is being measured has certain sides associated to it.
But, this is easier to show than explain, so here is a triangle:
And here is the angle associated with that triangle
Now, the side that is opposite of this angle is:
The side that is adjacent of this angle is:
And of course, the hypotenuse of this triangle is:
So, in SOHCAHTOA, the tangent of an angle is the opposite over the adjacent, or:
So, let’s see some examples:
Example 1:
15
20
35
Well, we remember from SOHCAHTOA that:
We can see that the side that is opposite of the angle is 15
And, we can see that the side that is adjacent to the angle is 20
So:
Or:
Example 2:
6
8
10
Well, we remember from SOHCAHTOA that:
We can see that the side that is opposite of the angle is 6
And, we can see that the side that is adjacent to the angle is 8
So:
Or:
Example 3:
9
10
Well, we remember from SOHCAHTOA that:
And, we can see that the side that is adjacent to the angle is 9
So:
NOW THAT THE REVIEW IS OVER
Let’s go over how to use tangent to find a missing side.
So, again, just like the cosine and sine functions, the tangent button on your calculator is used to find the ratio of certain angles.
See, each angle has its own special proportion.
The opposite side of that angle divided by the adjacent will always be a certain ratio, just like with Sine and Cosine.
So, here are some examples to help:
Example:
15
15
Well, we remember from SOHCAHTOA that:
We can see that the side that is opposite of the angle is 15
And, we can see that the side that is adjacent the angle is also 15
So:
Or:
Finding the missing side using Tangent
So to find the missing side using tangent, we need to have two things.
We need an angle (and it’s actual measurement),
And we need either the opposite side of the angle, or the adjacent side of the angle.
This is extremely similar to sine and cosine, but now instead of the hypotenuse, we are looking for the adjacent or opposite side.
Example 1:
Find the missing side of the triangle if:
5.7
The adjacent side = 5.7
So, we type into our calculators:
Then hit equal to get:
~1.73�Now we can set up the equation:
We know from SOHCAHTOA that:
Now we plug in what we know letting the unknown side be x:
5.7 * * 5.7
x = 9.86
Example 2:
Find the missing side of the triangle if:
3
The opposite side = 3
So, we type into our calculators:
Then hit equal to get:
~0.577�Now we can set up the equation:
We know from SOHCAHTOA that:
Now we plug in what we know letting the unknown side be x:
x * * x
0.577x = 3
______ _____
0.577 0.577
x = 5.2
EXAMPLE 3:
Find the missing side of the triangle if:
9
The adjacent side = 9
So, we type into our calculators:
Then hit equal to get:
0.488�Now we can set up the equation:
We know from SOHCAHTOA that:
Now we plug in what we know letting the unknown side be x:
9 * * 9
x = 4.39
Example 4:
Find the missing side of the triangle if:
2.7
The opposite side = 2.7
So, we type into our calculators:
Then hit equal to get:
1�Now we can set up the equation:
We know from SOHCAHTOA that:
Now we plug in what we know letting the unknown side be x:
x * * x
x = 2.7
Example 5:
Find the missing side of the triangle if:
7.6
The adjacent side = 7.6
So, we type into our calculators:
Then hit equal to get:
~11.43�Now we can set up the equation:
We know from SOHCAHTOA that:
Now we plug in what we know letting the unknown side be x:
7.6 * * 7.6
x = 86.87