1. Basic Trigonometry

2. Parts of a Right Triangle
The hypotenuse will always be the longest side, and opposite from the right angle.
Imagine that you are at Angle A looking into the triangle.
The opposite side is the side that is on the opposite side of the triangle from Angle A.
The adjacent side is the side next to Angle A.

3. Parts of a Right Triangle
Now imagine that you move from Angle A to Angle B.
From Angle B the opposite side is the side that is on the opposite side of the triangle.
From Angle B the adjacent side is the side next to Angle B.

4. Review B A B A For Angle A Hypotenuse This is the Opposite Side
This is the Adjacent Side A
Adjacent Side
Adjacent Side B
For Angle B
Hypotenuse
This is the Opposite Side
This is the Adjacent Side A

5. Trig Ratios Use Angle B to name the sides
Using Angle A to name the sides
We can use the lengths of the sides of a right triangle to form ratios. There are 3 different ratios that we can make.
The ratios are still the same as before!!

6. Trig Ratios Each of the 3 ratios has a name
Hypotenuse
Each of the 3 ratios has a name
The names also refer to an angle
Opposite A
Adjacent

7. Trig Ratios If the angle changes from A to B
Hypotenuse
If the angle changes from A to B
Opposite A
The way the ratios are made is the same
Adjacent

8. SOHCAHTOA B Hypotenuse
Here is a way to remember how to make the 3 basic Trig Ratios
Opposite A
Adjacent
1) Identify the Opposite and Adjacent sides for the appropriate angle
SOHCAHTOA is pronounced “Sew Caw Toe A” and it means
Sin is Opposite over Hypotenuse, Cos is Adjacent over Hypotenuse, and Tan is Opposite over Adjacent
Put the underlined letters to make
SOH-CAH-TOA

9. Examples of Trig Ratios
First we will find the Sine, Cosine and
Tangent ratios for Angle P. 20 12
Adjacent
Next we will find the Sine, Cosine, and
Tangent ratios for Angle Q Q 16
Opposite
Remember SohCahToa

10. Similar Triangles and Trig RatiosP B 20 12 5 3 A Q C 4 R 16
They are similar triangles, since ratios of corresponding sides are the same
Let’s look at the 3 basic Trig ratios for these 2 triangles
Notice that these ratios are equivalent!!

11. Similar Triangles and Trig Ratios
Triangles are similar if the ratios of the lengths of the corresponding side are the same.
Triangles are similar if they have the same angles
All similar triangles have the same trig ratios for corresponding angles