SOH-CAH-TOA EAST OF JAVA

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SOH-CAH-TOA EAST OF JAVA. [Exploring Trigonometric Functions]. SOH-CAH-TOA means many things. “Hello” “Goodbye” “I love you” “Your slip is showing” “It’s Your turn to take out the trash!!!”. SOHCAHTOA Also Means: “Let’s do Trig!!. [SOH] Sine – Opposite – Hypotenuse

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## SOH-CAH-TOA EAST OF JAVA

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### SOH-CAH-TOA EAST OF JAVA

[Exploring Trigonometric Functions]

Army Daniel

SOH-CAH-TOA means many things
• “Hello”
• “Goodbye”
• “I love you”
• “It’s Your turn to take out the trash!!!”

Army Daniel

SOHCAHTOA Also Means: “Let’s do Trig!!

[SOH] Sine – Opposite – Hypotenuse

[CAH] Cosine – Adjacent – Hypotenuse

[TOA] Tangent – Opposite - Adjacent

Army Daniel

First: A quick Geometry Review

PARTS

OF A

RIGHT

TRIANGLE

OPPOSITE

HYPOTENUSE

Army Daniel

SOH-CAH-TOA

Army Daniel

SOH: SINE-OPP-HYP

sin  = opposite side

hypotenuse

OPPOSITE

HYPOTENUSE

Army Daniel

SOH-CAH-TOA

Army Daniel

hypotenuse

OPPOSITE

HYPOTENUSE

Army Daniel

SOH-CAH-TOA

Army Daniel

tan  = opposite side

OPPOSITE

HYPOTENUSE

Army Daniel

A QUICK REVIEW

SOH - sin  = Opposite side

Hypotenuse

CAH - cos  = Adjacent side

Hypotenuse

TOA - tan  = Opposite side

Army Daniel

APPLICATIONS:

Let’s solve a problem.

Sohcahtoa!

Army Daniel

Check for Understanding.

Find

sin  =

cos  =

tan  =

5

3

4

Army Daniel

Check : Don’t Forget!

Find

sin  = OPP

HYP

HYP

tan  = OPP

3

5 HYP

4 OPP

Army Daniel

Find

sin  = OPP = 4

HYP 5

cos  = ADJ = 3

HYP 5

tan  = OPP = 4

3

5 HYP

4 OPP

Army Daniel

APPLICATIONS:

Let’s try a different problem.

Sohcahtoa!

Army Daniel

Check for Understanding.

Find x

given: cos 60° = 0.5

x

60°

1

Army Daniel

Check for Understanding.

Find x

given: cos 60° = 0.5

And don’t forget

SOH-CAH-TOA

x

60°

1

Army Daniel

X = 2

How?

x

60°

1

Army Daniel

X = 2

How? Use

SOH – CAH - TOA

cos 60° = .5 = ADJ = 1

HYP x

.5x = 1

x = 2

x

60°

1

Army Daniel

APPLICATIONS:

Let’s try a WORD problem!

Sohcahtoa!

Army Daniel

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?

Army Daniel

Find the Height of Mt. Sohcahtoa

What do we know?

• = 60°

Base = 6 miles = 3 miles

2

Height

6 miles

Army Daniel

What else do know?

SOH - sin  = Opposite side

Hypotenuse

CAH - cos  = Adjacent side

Hypotenuse

TOA - tan  = Opposite side

Which one should we use?

Height

6 miles

Army Daniel

Which one?

SOH - sin  = Opposite side

Hypotenuse

CAH - cos  = Adjacent side

Hypotenuse

TOA - tan  = Opposite side

Height

6 miles

Army Daniel

WHY??

tan  = Opposite side

tan 60°(3mi) = h .(3mi)

3 mi

(tan 60°)(3 miles) = h

(0.866)(3) = h

h = 2.598 miles

Height

h

3 miles

Army Daniel

WHY??

tan  = Opposite side

tan 60°(3mi) = h .(3mi)

3 mi

(0.866 )(3 miles) = h

Height

h= 2.598

3 miles

Army Daniel

WHY??

tan  = Opposite side

tan 60° = h .

3 miles

(tan 60°)(3 miles) = h

(0.866)(3) = h

h = 2.598 miles

Height

h

3 miles

Army Daniel

WHY??

tan  = Opposite side

tan 60° = h .

3 miles

(tan 60°)(3 miles) = h

(0.866)(3) = h

h = 2.598 miles

Height

h

3 miles

Army Daniel

EXCELLENT!!!

You deserve a HAND!

Now, Let’s Work!!!

SOHCAHTOA!!!

Army Daniel

Class Asignment:

pp. 356-359 Problems #’s 1 – 40

Homework:

p. 360 – 361 #’s 3 – 51 multiples of 3

ASSIGNMENT

Army Daniel

Resources
• Picture of Sohcahtoa:

[Devil’s Tower] http://www.animationfactory.com/free/nature/nature_page_aa.html

Army Daniel