Course Project Review/Preview
![Right Triangle](http://ugaemat6700.weebly.com/uploads/3/1/6/0/31605851/right_3_gif.gif)
Trigonometry - Measurement of Triangles
Let's remember the notation for a right triangle:
Move the triangle around and notice that the hypotenuse is always on the opposite side of the right angle |
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Pythagorean TheoremPythagorean theorem: c² = a² + b²
where c is the hypotenuse and a and b are the two legs of a right triangle By now, you probably already know the Pythagorean theorem and have used it, but if you need some practice, watch the Kahn Academy video and then practice HERE. |
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Trigonometric Ratios
You may have heard of this before. Remember that trigonometric means triangle measure, and a ratio is simply a way to show how two values are related. Therefore, trigonometric ratios show how two measures of a triangle are related. Let's look at some definitions:
In right triangle trigonometry, the opposite side and the adjacent side will NEVER be the hypotenuse. Opposite and adjacent sides always refer to legs of a triangle.
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Once you are comfortable with the above terms, consider these three important terms:
These are extremely simple because they refer to ratios of a right triangle
- Sine (Abbreviated Sin)
- Cosine (Abbreviated Cos)
- Tangent (Abbreviated Tan)
These are extremely simple because they refer to ratios of a right triangle
These ratios are easy to remember with the right mnemonic device. Listed below are some examples you can remember, or you may create your own:
To practice, use the Kahn Academy applet.
Once you are comfortable with the trigonometric ratios, draw three diffrently oriented right triangles.
Give them all different side lengths. Remember which side is supposed to be the longest!
Pick one angle on each triangle and find its three trigonometric ratios.
Now draw a triangle like the one in the applet above. Imagine that it represents a side of a house with a ladder leaning against it. Label the side of the house, the ground, and the ladder. What would happen if the ladder were shorter than the height of the house? Could you get to the roof?
Stop here and allow the teacher to check your work before proceeding to the Unit Circle Activity.
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To practice, use the Kahn Academy applet.
Once you are comfortable with the trigonometric ratios, draw three diffrently oriented right triangles.
Give them all different side lengths. Remember which side is supposed to be the longest!
Pick one angle on each triangle and find its three trigonometric ratios.
Now draw a triangle like the one in the applet above. Imagine that it represents a side of a house with a ladder leaning against it. Label the side of the house, the ground, and the ladder. What would happen if the ladder were shorter than the height of the house? Could you get to the roof?
Stop here and allow the teacher to check your work before proceeding to the Unit Circle Activity.