Name: Date: Similarity: Trigonometric Ratios
[Pages:3]Name:____________________
Date:_______________
Similarity: Trigonometric Ratios
We already know that any right triangle with a given acute angle is similar to every other
right triangle with that same acute angle measure (AA Postulate).
We can use the AA Postulate to discover properties of the
A D
angles in the triangle:
Example: CD intersects right triangle, ABC. Identify
whether ABC~CBD~ACD
C
B
Notice that CBD and ACD are also right triangles
C
ABC ~ ACD because of AA: m A = m A; m C = m D. ABC ~ CBD because of AA: m B = m B; m D = m C A D CBD ~ ACD because of AA: m C = m C; m D = m D
Therefore, ABC~CBD~ACD
C
A
B
D
C
B
Trigonometric ratios are established ratios used to find the acute angle measures in right triangles. For example, to find the m A in ABC above, apply the trigonometric ratio, sine, to compare the values of opposite leg a to hypotenuse c.
Sin A = CB/AB
If the measurement of a is unknown, use cosine to compare the values of the adjacent leg to
the hypotenuse: Cos A = AC/CB
A summary of these ratios, their shortenings (how they appear on your calculator), and the values they compare are listed below. Note that theta () is a Greek symbol used to represent the unknown angle.
Trigonometric Ratio Sine
Cosine
Shortening sin
cos
Values Compared
Opposite leg Hypotenuse
Adjacent Leg Hypotenuse
Name:____________________
Practice. Identify the sine or cosine.
1.sin =
A
6
C
24 B
3. sin =
8
Date:_______________
2. cos =
A
C A
4. Sin =
10
8
3
B
6
C
5
B
5. cos = 12
24
6. sin =
A
25 15
C
B
7. sin =
A
32
8. cos =
8
4
9. cos =
C
B
15
20
10. sin =
36
27
Name:____________________
Answer Key
Date:_______________
Similarity: Trigonometric Ratios
1. sin = ? 2. cos = 3/8 3. sin = 3/5 4. sin = 10/52 = 22 5. cos = 22 6. sin = 15/25 = 3/5 7. sin = 3/32 = 2/2 8. cos = ? 9. cos = 4/5 10. sin = 4/5
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