Transcript Basic Trigonometry

Basic Trigonometry
Parts of a Right Triangle
B
Hypotenuse
Opposite Side
C
A
Adjacent Side
The hypotenuse will always be the
longest side, and opposite from the
right angle.
The adjacent side is the side next
to Angle A.
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.
Parts of a Right Triangle
B
Hypotenuse
Opposite Side
C
A
Adjacent Side
Now imagine that you move from
Angle A to Angle B.
From Angle B the adjacent side is
the side next to Angle B.
From Angle B the opposite side is
the side that is on the opposite side
of the triangle.
B
Review
For Angle A
Hypotenuse
This is the Opposite Side
Opposite Side
Opposite Side
This is the Adjacent Side
A
Adjacent
Adjacent Side
Side
For Angle B
B
Hypotenuse
This is the Opposite Side
This is the Adjacent Side
A
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.
B
Hypotenuse
Opposite
C Adjacent
The ratios are still the same as before!!
Opposite
Hypotenuse
Adjacent
Hypotenuse
Opposite
Adjacent
A
Trig Ratios
• Each of the 3 ratios has a name
• The names also refer to an angle
Hypotenuse
Opposite
A
Adjacent
Sine of Angle A =
Opposite
Hypotenuse
Cosine of Angle A =
Adjacent
Hypotenuse
Opposite
Tangent of Angle A =
Adjacent
Trig Ratios
B
If the angle changes from A to B
The way the ratios are made is the
same
Sine of Angle B =
Opposite
Hypotenuse
Cosine of Angle B =
Adjacent
Hypotenuse
Tangent of Angle B =
Opposite
Adjacent
Hypotenuse
Opposite
A
Adjacent
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
2) 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
Examples of Trig Ratios
First we will find the Sine, Cosine and
Tangent ratios for Angle P.
Next we will find the Sine, Cosine, and
Tangent ratios for Angle Q
P
20
12
Adjacent
16
Opposite
Remember SohCahToa
16
20
Sin P

Cos P
12

20
Tan P
16

12
Sin Q

12
20
Cos Q

16
20
Tan Q

12
16
Q
Similar Triangles and Trig Ratios
P
B
20
12
5
3
Q
R
C
16
ABC  QPR
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
Sin Q

12
20
Cos Q

16
20
Tan Q

12
16
A
4

3
5
Cos A

4
5
Tan A

3
4
Sin A
Notice that these ratios are equivalent!!
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