RIGHT TRIANGLE TRIGONOMETRY!!

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Home Page Basic Constructions and Unknown Angles Triangle Proofs

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Let's start with the basics!

When we label a triangle, we have to figure out which side is which:
1. The hypotenuse is the side across from the right angle
2. The opposite is the side across from the specified acute angle
3. The adjacent is the side included between the right angle and the specified acute angle
So a labeled diagram would look like:

So now we want to know how to solve the problems:

If it is a sine problem, you will have an opposite side and a hypotenuse side given to you
If it is a cosine problem, you will have an adjacent side and a hypotenuse side given to you
If it is a tangent problem, you will have an opposite side and an adjacent side given to you

After you have determined whether it is a sine, cosine, or a tangent problem, follow this chart:

Now if you are going to solve for an unknown side, you have to substitute your figure information inside an equation:

If you are trying to solve for an unknown side FOR SINE, your equation will be: sin(angle measure)=opposite/hypotenuse
If you are trying to solve for an unknown side FOR COSINE, your equation will be: cos(angle measure)=adjacent/hypotenuse
If you are trying to solve for an unknown side FOR TANGENT, your equation will be: tan(angle measure)=opposite/adjacent

IF THE UNKNOWN SIDE IS THE NUMERATOR, YOU WILL MULTIPLY: X=sin/cos/tan(angle measure) x given side
IF THE UNKNOWN SIDE IS THE DENOMINATOR, YOU WILL DIVIDE: X=given side / sin/cos/tan(angle measure)
*Make sure your calculator is in degree mode*

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Now if you are going to solve for an unknown angle, you have to substitute your figure information inside an equation:

If you are trying to solve for an unknown angle FOR SINE, your equation will be: sin^-1(angle measure)=opposite/hypotenuse
If you are trying to solve for an unknown angle FOR COSINE, your equation will be: cos^-1(angle measure)=adjacent/hypotenuse
If you are trying to solve for an unknown angle FOR TANGENT, your equation will be: tan^-1(angle measure)=opposite/adjacent

*Make sure your calculator is in degree mode*

Solve these problems:

Here are the answers:

What common issues do students have when learning this topic, what strategies/analogies have you learned that could be used to understand this topic better, how does this topic relate to the world outside of school?
Some common issues that students have is that they don't remember how to label the diagram. They might mistakingly use cosine instead of sine. A good strategy to remember which trig function to use, is using SOH CAH TOA. This topic can be used for architectural building. All the key measurements are in the problem itself.