1. SOH-CAH-TOA EAST OF JAVA
[Exploring Trigonometric Functions]
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2. SOH-CAH-TOA means many things
“Hello”
“Goodbye”
“I love you”
“Your slip is showing”
“It’s Your turn to take out the trash!!!”
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3. SOHCAHTOA Also Means: “Let’s do Trig!!
[SOH] Sine – Opposite – Hypotenuse
[CAH] Cosine – Adjacent – Hypotenuse
[TOA] Tangent – Opposite - Adjacent
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4. First: A quick Geometry Review
PARTS
OF A
RIGHT
TRIANGLE
OPPOSITE
HYPOTENUSE
ADJACENT
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5. So, Sohcahtoa! […trans. “Let’s do Trig.!”]
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6. We’ll break it into syllables.
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7. SOH-CAH-TOA
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8. SOH: SINE-OPP-HYP sin  = opposite side hypotenuse OPPOSITE HYPOTENUSE
ADJACENT
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9. SOH-CAH-TOA
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10. CAH: COSINE-ADJ-HYP cos  = adjacent side hypotenuse OPPOSITE
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11. SOH-CAH-TOA
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12. TOA: TAN-OPP-ADJ tan  = opposite side adjacent OPPOSITE HYPOTENUSE
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13. A QUICK REVIEW SOH - sin  = Opposite side Hypotenuse
CAH - cos  = Adjacent side
TOA - tan  = Opposite side
Adjacent side
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14. APPLICATIONS:
Let’s solve a problem.
Sohcahtoa!
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15. Check for Understanding.
Find
sin  =
cos  =
tan  = 5 3 4
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16. Check : Don’t Forget! Find sin  = OPP HYP cos  = ADJ 3 ADJ
tan  = OPP
ADJ 3
ADJ
5 HYP
4 OPP
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17. Check : ANSWERS Find sin  = OPP = 4 HYP 5 cos  = ADJ = 3 3 ADJ
tan  = OPP = 4
ADJ 3
ADJ
5 HYP
4 OPP
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18. APPLICATIONS:
Let’s try a different problem.
Sohcahtoa!
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19. Check for Understanding.
Find x
given: cos 60° = 0.5 x
60° 1
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20. Check for Understanding.
Find x
given: cos 60° = 0.5
And don’t forget
SOH-CAH-TOA x
60° 1
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21. Check : ANSWER
X = 2
How? x
60° 1
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22. Check : ANSWER How? Use SOH – CAH - TOA cos 60° = .5 = ADJ = 1 HYP x x
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23. APPLICATIONS:
Let’s try a WORD problem!
Sohcahtoa!
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24. Find the Height of Mt. Sohcahtoa
The volcano is rumbling. The Sohcahtoans need to sacrifice a virgin. They know the base of the mountain is 6 miles high. The angle formed from the base to the top is 60°.
How tall is the mountain?
[Use your calculator!!!]
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25. Find the Height of Mt. Sohcahtoa
What do we know?
= 60°
Base = 6 miles = 3 miles 2
Height
6 miles
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26. What else do know? Height 6 miles SOH - sin  = Opposite side
Hypotenuse
CAH - cos  = Adjacent side
TOA - tan  = Opposite side
Adjacent side
Which one should we use?
Height
6 miles
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27. Which one? Height 6 miles SOH - sin  = Opposite side Hypotenuse
CAH - cos  = Adjacent side
TOA - tan  = Opposite side
Adjacent side
Height
6 miles
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28. WHY?? Height h 3 miles tan  = Opposite side Adjacent side
tan 60° (3mi) = h . (3mi)
3 mi
(tan 60°)(3 miles) = h
(0.866)(3) = h
h = miles
Height h
3 miles
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29. WHY?? Height h= 2.598 3 miles tan  = Opposite side Adjacent side
tan 60° (3mi) = h . (3mi)
3 mi
(0.866 )(3 miles) = h
answer h = miles
Height
h= 2.598
3 miles
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30. WHY?? Height h 3 miles tan  = Opposite side Adjacent side
tan 60° = h
3 miles
(tan 60°)(3 miles) = h
(0.866)(3) = h
h = miles
Height h
3 miles
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31. WHY?? Height h 3 miles tan  = Opposite side Adjacent side
tan 60° = h
3 miles
(tan 60°)(3 miles) = h
(0.866)(3) = h
h = miles
Height h
3 miles
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32. You deserve a HAND! Now, Let’s Work!!! SOHCAHTOA!!! EXCELLENT!!!
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33. ASSIGNMENT Class Asignment: pp. 356-359 Problems #’s 1 – 40 Homework:
p. 360 – 361 #’s 3 – 51 multiples of 3
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34. Resources Picture of Sohcahtoa:
[Devil’s Tower]
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