Geometry Notes Day 1
7.5-7.6 Trig Ratios (SOH CAH TOA)
1.
Name____________
a. What leg is opposite ∠ B?
A
b. What side is the hypotenuse?
c. What leg is adjacent to ∠ B ? (remember a leg can’t be the hypotenuse)
B
C
Based on the pictures in #3 and #4, answer each of the following.
2. a. Are the triangles in #3 and #4 similar?
b. Because similar triangles have corresponding angles that are ________________, we
know that:
_____ ≅ _____, _____ ≅ _____, and _____ ≅ _____
3.
D
3
F
5
4
E
4.
G
15
From ∠ D…
a. What is the length
of the opposite leg?
From ∠ D…
(give answers in fractions and as rounded decimals)
d. What is the ratio of the opposite leg to
the hypotenuse?
b. What is the length
of the hypotenuse?
e. What is the ratio of the adjacent leg to
the hypotenuse?
c. What is the length
of the adjacent leg?
f. What is the ratio of the opposite leg to
the adjacent leg?
From ∠ G…
a. What is the length
of the opposite leg?
From ∠ G… (give answers in fractions and decimals)
d. What is the ratio of the opposite leg to
the hypotenuse?
b. What is the length
of the hypotenuse?
e. What is the ratio of the adjacent leg to
the hypotenuse?
c. What is the length
of the adjacent leg?
f. What is the ratio of the opposite leg to
the adjacent leg?
9
L
12
H
Each of the ratios from #3 are equal to each of the ratios from #4.
Explain why you think this is true:
Trigonometry is the study of angles and side lengths in a triangle. A trigonometric ratio is a
ratio of the lengths of two sides of a right triangle. These ratios are given specific names.
Trig Ratios: A way to remember the ratios is to use the acronym: SOH CAH TOA
Name
Abbreviation Ratio of sides…
A
length of leg opposite ∠A
Sine
sin
sin(A) =
Cosine
length of hypotenuse
length of leg adjacent to ∠A
cos(A) =
length of hypotenuse
length of leg opposite of ∠A
tan(A) =
length of leg adjacent to ∠A
cos
Tangent tan
hypotenuse
leg adjacent
to A
C
leg opposite of
A
B
Complete each ratio using the picture below.
1. sin(30) =
30º
3
2. tan(30) =
6
3. cos(60) =
60º
3
6. ____(60) =
3
5. cos(____) =
6
7. _____(60) =
8. cos(____) =
6
4. tan(____) =
3
3
3 3
3
6
9. tan(____) =
10. cos(___) =
3 3
3
1
think simplified fraction!
2
3
3
3
2
think simplified fraction!
think simplified fraction!
Find the indicated trig.ratio of sides as a fraction and as a decimal (rounded to the nearest 100th).
11. Sin ! B =
12. Cos ! D =
13. Tan ! D =
A
16
8
D
14. Sin ! DAC=
15. Tan ! B =
8
C
B
16. Cos ! BAC=
Trig functions on your Scientific Calculator. Your calculator has the ratios stored!!
Determine the value of each ratio, using your calculator. Round to the nearest hundredth:
17.
Sin (60o)
18.
Tan (45o)
19.
Cos (30o)
20.
Tan (52o)
21.
Sin (64o)