Transcript What side is adjacent to A?

A
C
Warm UP
B
What side is The hypotenuse?
Line AB (purple)
What side is opposite  A?
Line CB (red)
What side is adjacent to  A?
Line AC (blue)
What side is opposite  B?
Line AC (blue)
What side is adjacent to  B?
Line CB (red)
Trigonometric Ratio
The Ratio of two sides of a triangle
There are 3 trigonometric ratios:
Sine: Opposite over the hypotenuse
Cosine: Adjacent over the hypotenuse
Tangent: Opposite over the adjacent
SohCahToa
Sine
(sin)
Opposite
Hypotenuse
A
Sin A =
CB
AB
Sin B =
AC
AB
C
B
Cosine
(cos)
Cos A =
adjacent
Hypotenuse
A
AC
AB
CB
Cos B = AB
C
B
Tangent
(tan)
tan A =
CB
AC
tan B =
AC
CB
Opposite
adjacent
A
C
B
Find the sine, cosine, and tangent of each angle
16
sin A = 20
12
Cos A =
20
16
tan A = 12
12
sin B = 20
Cos B = 16
20
12
tan B = 16
A
= 4
5
3
=
5
4
=
3
3
=
5
= 4
5
3
=
4
20
12
C
B
16
Look at the sin of A and the cos of B.
Do you notice anything?
Look at tan A and tan B.
We will never do this with a right angle.
Your calculator or a trig table gives
you the trigonometric ratio for every
possible angle of a triangle.
• Always make sure your calculator is set in
degrees before starting any problem.
• Try these: ( round to 4 decimal places)
1) sin 30° =
2) cos 25° =
0.5
.9063
3) tan 45° =
1
4) sin 78° =
.9781
Remember that these values
represent the ratio of the
sides of the triangle.
sin (A) =
Opposite
hypotenuse
cos (A) =
Adjacent
hypotenuse
tan (A) =
opposite
adjacent
If you know one side and an angle
you can use the trigonometric ratio
to find the other side by writing a
proportion
75°
x
25
X is adjacent to the 75 degree angle and 25
is the hypotenuse so we will use Cosine
cos 75= X
25
1
25 cos 75 = x
25 (.2588) = x
6.4705 = x
6.5= x
This doesn’t look like
a proportion does it?
How about now?
Using a calculator
Round to the nearest tenth
Identify which trig function you would use to solve
for the x
x
25
x
20°
25°
x
16
sin
cos
65°
tan
6
sin
32°
tan
x
20
cos
24
68°
x
35
x
70°
When the variable is on the bottom
don’t panic!
x
Remember when life was
easy and you and you did
problems like this:
4= 20
x
Multiply by x on both sides
4x = 20
Now divide by 4 on both sides
x= 20
4
See how the x and the 4 just switch places.
That always happens. (That’s what I love
about math)
25°
16
cos 25= 16
x
Put this in your
16
x=
calculator.
cos 25
x=17.6540
X =17.7
Now solve for x
32°
x
24
68°
x= 32.0067
x = 32.0
x
70°
20
tan 32= 20
x
x= 20
tan 32
x
35
cos 68= x
24
24 cos 68 = x
8.9905 = x
9.0 = x
sin 70= 35
x
x= 35
sin 70
x= 37.2462
x = 37.2