Algebra Review - Right Triangles and Trigonometry

1. Similar Triangles

Similar triangles have the same "shape" but not the same size. They also have the same angle measures. Corresponding angles are the angle pairs that are the same in a triangle. Corresponding sides are similar. Look at the example below:

           

Here are two triangles that are similar. ∆ABC is similar to ∆MNO. The following table lists their corresponding sides and corresponding angles.

Corresponding Angles

Corresponding Sides

A and M

x and e

B and N

y and f

C and O

z and g

In similar triangles, the lengths of the corresponding sides are proportional. For example, let x = 18, y = 9, and z = 21. Then in a similar triangle, e = 12, f = 6, g = 14.

If you turn them into a ratio, they would all have the same ratios:

       

Right triangles are similar if either one of their smaller angles are the same. All right triangles have a 90 angle.


2. Trigonometric Ratios

That is how the legs are called when you refer to the angle B. The side directly opposite is called the opposite. The hypotenuse is always the longest side, and the side adjacent is always called the adjacent.

If you refer to angle C, the opposite side would be AB, and the adjacent would be AC.

The Sine, The Cosine, and The Tangent

The following are the trigonometric ratios:

A method to remember them easily is to use the phrase "Oh, Heck, Another Hour Of Algebra!"

Oh, Heck = sine = opposite over hypotenuse
Another Hour = cosine = adjacent over hypotenuse
Of Algebra = tangent = opposite over adjacent


That's basically about it for the trigonometric ratios. If you need help figuring out how to use them, just ask the staff.

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