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First Full TRIG day SIN COS TAN

Last updated over 1 year ago
16 questions

Make sure to label all three sides first. It will help out a lot. You will get the hang of it and then be able to start flying through it. But you have to label the 3 sides first.

The hypotenuse is the longest side of the right triangle. It is always the side that is across from the right angle. Think of the right angle box mark as an arrow that always points at the hypotenuse.


Always figure out which one is the hypotenuse first. It will help figuring out the other 2 next.

After the hypotenuse find the adjacent side. It is the other side that touches the angle you are dealing with.

The last side is obviously going to be the opposite. It is the only one that is left. It is the side that doesn't touch the angle at all.
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Notice this says tan of angle A.
remember tan = Opposite/Adjacent

Label all three sides first.
Remember figure the hypotenuse first. Here the hypotenuse is the side that is 34 long. We don't need that for tan, but you still need to figure that out first.

Next find the adjacent side. Adjacent to angle A in this case, because that is the angle it tells us at the top of the problem. The adjacent side is the other side that touches angle A. which is 16. So the adjacent is 16.

Last find the opposite side. It is the only one that is left. It is the 30. It is the only side that does not touch angle A. So the opposite is 30.

So again tan = opposite/adjacent

So opposite is 30 adjacent is 16
the tangent of angle A is going to be

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cos = adjacent/hypotenuse

First find the hypotenuse.
the hypotenuse is 15.

Next find the adjacent side. It is the other side that touches angle C. Which is the 12 side.
So adjacent is 12.

Last find the opposite. It is the only other side. The 9 side. It is the only side that doesn't touch angle C.

H=15
A=12
O=9

cos = adjacent / hypotenuse

12 / 15

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sin = opposite/hypotenuse

First find the hypotenuse.
the hypotenuse is 20.

Next find the adjacent side. It is the other side that touches angle Z. Which is the 16 side.
So adjacent is 16.

Last find the opposite. It is the only other side. The 12 side. It is the only side that doesn't touch angle Z.

H=20
A=16
O=12

sin = opposite / hypotenuse
12 / 20

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Notice on this one they have turned the triangle on its hypotenuse. You are looking for the cosine of angle A.
cos is adjacent over hypotenuse.

Label all the sides first.
Hypotenuse is the 45. Notice how the red right angle mark is like an arrow head pointing at that side of 45.
Next the adjacent is the other side that touches angle A.
That is the 36 side.
Last the opposite. Its the only one left. It is the 27.
H=45
A=36
O=27

Adjacent / Hypotenuse

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On these last 3 problems we are going to be finding the length of the missing side.
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Angle A is the angle we are focusing on because it has the angle measurement in it. 41°

First lets label sides for Angle A.

Hypotenuse is the blank side.
Adjacent is the side with x.
Opposite is the side with 4.

Next what function do we need?
Ok first think about the blank side. It is the hypotenuse. That side doesn't give me anything that I don't want or need. So the other 2 sides are the sides I care about. The adjacent side and the opposite sides are the 2 sides I need for this problem.
So what function uses adjacent and opposite?
SOH CAH TOA.
It is the tangent function.
I will be using the tangent function here.

And tangent is opposite/adjacent
4 / x

So just to set it up it will look like this.

Remember from the last day when the x is on the bottom we will be dividing the numbers.
In the calculator it looks like this

remember to always click on "deg"

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Angle B is the angle we are focusing on because it has the angle measurement in it. 57°

Hypotenuse is x.
Adjacent is blank.
Opposite is 10.8.

Since the adjacent side is the one that is blank that is the side I won't be using at all in this problem.
The hypotenuse and the opposite are the sides that I want.

Which function uses opposite and hypotenuse? sin, cos or tan?

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