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This is a right triangle. The red line is called the hypotenuse. It is opposite from the right angle (90 degrees).



In a simple explanation, sine, cosine, and tangent are each a ratio of sides in a right triangle.

A helpful name to remember each ratio is with the abbreviation, SOH CAH TOA. We'll go through each one.

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SOH (Sine)

SOH stands for Sine = Opposite/Hypotenuse.

The opposite is the side across from the angle. For example, in the picture above, the opposite of angle C is line AB.

The hypotenuse is the side across from the right angle. For example, in the picture above, the hypotenuse of the triangle is line AC.

So, sin C = AB/AC
Substituting the values from the triangle,
sin C = 3/5

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CAH (Cosine)

CAH stands for Cosine = Adjacent/Hypotenuse.

The adjacent is the side next to the angle, not including the hypotenuse (the hypotenuse is described as the hypotenuse). For example, the adjacent of angle C is line BC, because it is next to angle C.

The hypotenuse is the side across from the right angle. For example, in the picture above, the hypotenuse of the triangle is line AC.

So, sin C = BC/AC
Substituting the values from the triangle,
cos C = 4/5

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TOA (Tangent)

TOA stands for Tangent = Opposite/Adjacent.

The opposite is the side across from the angle. For example, in the picture above, the opposite of angle C is line AB.

The adjacent is the side next to the angle, not including the hypotenuse (the hypotenuse is described as the hypotenuse). For example, the adjacent of angle C is line BC, because it is next to angle C.

So, tan C = AB/BC
Substituting the values from the triangle,
tan C = 3/4

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So what can you do with these? Let's look at an example trig problem:


For this example, we will be trying to solve for side AC. Let AC be x.

We will use tan to find it and plug in what we know.

tan() = opposite / adjacent

Plug in the numbers from the problem
tan(35) = 8 / x

Multiplying both sides by x, we get
x tan(35) = 8

Dividing both sides by tan(35), we get
x = 8/tan(35)

Now, put 8/tan(35) in a calculator.
The answer is approx. 11.42518405

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Hope this helps. Again, this not an extensive explanation and doesn't really show how to use it on Scratch.

Edit: corrected “SOH stands for Sine = Opposite/Adjacent.” to “SOH stands for Sine = Opposite/Hypotenuse.”