Exploring SOH CAH TOA
1. Draw a triangle on the CENTER of your grid paper using
the dimensions on your card. Be sure to draw the picture
like the following.
C
B
x
A
2. Find the length of the hypotenuse and label on your picture. (HINT: Use Pythagorean
Theorem)
3. Using your protractor, measure angle x and label inside the triangle. Be as accurate as
possible!
4. Fill in the table of ratios of lengths of the sides of the triangle:
B
A
B
C
A
C
Fraction Form
Decimal Form
5. Now look at your calculator. Change the mode to degree by pressing MODE and
selecting DEGREE.
6. Look above the numbers. There are buttons labeled SIN, COS, and TAN. We are about
use those! Yeah!
7. Fill in the table for angle x. Write answer as a decimal. For example, if you wanted to find
sin (30), you would type SIN, 30, ENTER in your calculator!
sin(x)
cos(x)
tan(x)
8. Now, match up the side ratios from the first chart with the corresponding trig expression
(sin, cos, or tan).
sin(x) = _____________
cos(x) = ________________ tan(x) = ________________
9. Compare with your partner. Did you guys get the same matches? If not, someone made a
mistake someone! Please fix it!
10. So, if we labeled a triangle as shown, fill in the following general formulas (with words
instead of letters).
Hypotenuse
(C)
Opposite
(B)
cos(x)
x
Adjacent
(A)
sin =
cos =
sin(x)
tan(x)
tan=
Let’s practice some problems!
Find tan A and tan B. Write each answer as a decimal rounded to four decimal places.
1.
2.
tan A________
tan A ________
tan B ________
tan B ________
Find the sine and cosine ratios.
3.
sin z  =______
cos z  =______
sin x  =______
cos x  =________
82
18
z
80
4.
x
18
82
80
Find the value of x to the nearest tenth.
5. x = __________
6. x = _______
Use a sine or cosine ratio to find the value of each variable.
7.
.
26
8.
30 
x
18
y
x
32
y
x = ___________
x = ___________
y = ___________
y = ___________
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Leg length = 10 units
Leg length = 24 units
Leg length = 10 units
Leg length = 24 units
Leg length = 10 units
Leg length = 24 units
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Leg length = 5 units
Leg length = 12 units
Leg length = 5 units
Leg length = 12 units
Leg length = 5 units
Leg length = 12 units
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Leg length = 8 units
Leg length = 15 units
Leg length = 8 units
Leg length = 15 units
Leg length = 8 units
Leg length = 15 units
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Leg length = 3 units
Leg length = 4 units
Leg length = 3 units
Leg length = 4 units
Leg length = 3 units
Leg length = 4 units
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Leg length = 9 units
Leg length = 12 units
Leg length = 9 units
Leg length = 12 units
Leg length = 9 units
Leg length = 12 units
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Draw a right triangle with
the following:
Leg length = 6 units
Leg length = 8 units
Leg length = 6 units
Leg length = 8 units
Leg length = 6 units
Leg length = 8 units