1. A B C Warm UP What side is The hypotenuse? What side is opposite  A?
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)

2. SohCahToa 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

3. Sine (sin)
Opposite Hypotenuse A C B CB
Sin A = AB AC
Sin B = AB

4. Cosine (cos)
adjacent Hypotenuse A C B AC
Cos A = AB CB
Cos B = AB

5. Tangent (tan)
Opposite adjacent A C B CB
tan A = AC AC
tan B = CB

6. Find the sine, cosine, and tangent of each angleB 12 16 20 16 20 4 5
sin A = = 20 12 5 3
Cos A = = 16 12 4 3
tan A = =
Look at the sin of A and the cos of B.
Do you notice anything?
Look at tan A and tan B. 20 12 5 3
sin B = = 16 20 4 5
Cos B = =
We will never do this with a right angle. 12 16 3 4
tan B = =

7. 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)
Remember that these values represent the ratio of the sides of the triangle.
sin 30° =
cos 25° =
tan 45° =
sin 78° =
0.5
.9063
Opposite hypotenuse
sin (A) = 1
Adjacent hypotenuse
cos (A) =
.9781
opposite adjacent
tan (A) =

8. If you know one side and an angle you can use the trigonometric ratio to find the other side by writing a proportion
X is adjacent to the 75 degree angle and 25 is the hypotenuse so we will use Cosine x
75° 25
This doesn’t look like a proportion does it?
X 25
cos 75=
How about now? 1
25 cos 75 = x
25 (.2588) = x
Using a calculator
= x
6.5= x
Round to the nearest tenth

9. Identify which trig function you would use to solve for the x6
65° x 25
20° x 16
25°
sin
cos
tan
70° 35 x
32° 20 x
sin
tan
cos
68° x 24

10. When the variable is on the bottom don’t panic!x 16
25°
Remember when life was easy and you and you did problems like this: 4=
20 x
cos 25=
16 x
Multiply by x on both sides
Put this in your calculator. x=
16 cos 25
4x = 20
Now divide by 4 on both sides x= x=
20 4
X =17.7
See how the x and the 4 just switch places.
That always happens. (That’s what I love about math)

11. Now solve for x x 24 35 x 20 x cos 68= sin 70= tan 32= 35 sin 70
70° 35 x
32° 20 x
68° x 24
sin 70=
35 x
tan 32=
20 x
cos 68=
x 24 x=
20 tan 32 x=
35 sin 70
24 cos 68 = x
= x x= x=
9.0 = x
x = 37.2
x = 32.0