7.5 & 7.6– apply the sin-cos-tan ratios. hypotenuse: opposite side: adjacent side: side...
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7.5 & 7.6– Apply the Sin-Cos-Tan Ratios
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Hypotenuse:
Opposite side:
Adjacent side:
Side opposite the reference angle
Side opposite the right angle
Side touching the reference angle, but not the hypotenuse
A
hypotenuse
opp
osit
e
adjacent
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a
b
c
A
B
C
sin cos tan
sin A° = opphyp cos A° =
adjhyp tan A° =
oppadj
sin A° = ac cos A° =
bc tan A° =
ab
S O H C A H T O A
Note: You cannot use trig ratios on the right angle
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1. Find the sin R. Write your answer as a fraction.
sin R° = 1517
SOH – CAH – TOA
A
H
O
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2. Find the cos A. Write your answer as a fraction.
cos A° = 1620
SOH – CAH – TOAA
H
O
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3. Find the tan B. Write your answer as a fraction.
tan B° = 24.
10
SOH – CAH – TOA
A
H
O
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4. Write the trigonometric ratio as a decimal to two decimal places.
a. sin 62° b. cos 25° c. tan 38°
0.88 0.91 0.78
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5. Solve for x. Round to two decimal places.
1
x = 5 sin 24°
x = 2.03
sin 245
x a.
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5. Solve for x. Round to two decimal places.
x
435tan
1
x tan35° = 4tan35° tan35°
x = 5.71
b.
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Steps to solving with trig:
1.
2.
3.
4.
Label the sides with the reference angle
Choose a side to solve for
What side do you know and what side are you solving for?
Identify which trig ratio to use
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cos 50° = a .
10
10 cos 50° = a
6.43 = a
A
H
6. Approximate the missing side length to two decimal places.
SOH – CAH – TOA
1
O
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sin 42° = c .
7
7 sin 42° = c
4.68 = c
SOH – CAH – TOA
1A
HO
6. Approximate the missing side length to two decimal places.
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m n
tan 39° = 25m
m tan 39° = 25
m = 30.87
SOH – CAH – TOA
1sin 39° =
25n
n sin 39° = 25
n = 39.73
1
tan 39° tan 39° sin 39° sin 39°
A
H
O
7. Approximate the missing side lengths to two decimal places.
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t u
sin 51° = t .
32
32 sin 51° = t
24.87 = t
SOH – CAH – TOA
1cos 51° =
u .
32
32 cos 51° = u
20.14 = u
1
A
H
O
7. Approximate the missing side lengths to two decimal places.
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a b
tan 57° = 14 a
a tan 57° = 14
SOH – CAH – TOA
1
tan 57° tan 57°
a = 9.09
sin 57° = 14 b
b sin 57° = 14
1
sin 57° sin 57°
b = 16.69
A
H
O
7. Approximate the missing side lengths to two decimal places.
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m n
cos 31° = 79m
m cos 31° = 79
SOH – CAH – TOA
1
cos 31° cos 31°
m = 92.16
tan 31° = n .
79
79 tan 31° = n
1
n = 47.47
A
H
O
7. Approximate the missing side lengths to two decimal places.