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**SOH-CAH-TOA EAST OF JAVA**

[Exploring Trigonometric Functions] Army Daniel

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**SOH-CAH-TOA means many things**

“Hello” “Goodbye” “I love you” “Your slip is showing” “It’s Your turn to take out the trash!!!” Army Daniel

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

[SOH] Sine – Opposite – Hypotenuse [CAH] Cosine – Adjacent – Hypotenuse [TOA] Tangent – Opposite - Adjacent Army Daniel

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**First: A quick Geometry Review**

PARTS OF A RIGHT TRIANGLE OPPOSITE HYPOTENUSE ADJACENT Army Daniel

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**So, Sohcahtoa! […trans. “Let’s do Trig.!”]**

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**We’ll break it into syllables.**

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SOH-CAH-TOA Army Daniel

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**SOH: SINE-OPP-HYP sin = opposite side hypotenuse OPPOSITE HYPOTENUSE**

ADJACENT Army Daniel

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SOH-CAH-TOA Army Daniel

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**CAH: COSINE-ADJ-HYP cos = adjacent side hypotenuse OPPOSITE**

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SOH-CAH-TOA Army Daniel

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**TOA: TAN-OPP-ADJ tan = opposite side adjacent OPPOSITE HYPOTENUSE**

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**A QUICK REVIEW SOH - sin = Opposite side Hypotenuse**

CAH - cos = Adjacent side TOA - tan = Opposite side Adjacent side Army Daniel

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APPLICATIONS: Let’s solve a problem. Sohcahtoa! Army Daniel

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**Check for Understanding.**

Find sin = cos = tan = 5 3 4 Army Daniel

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**Check : Don’t Forget! Find sin = OPP HYP cos = ADJ 3 ADJ**

tan = OPP ADJ 3 ADJ 5 HYP 4 OPP Army Daniel

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**Check : ANSWERS Find sin = OPP = 4 HYP 5 cos = ADJ = 3 3 ADJ**

tan = OPP = 4 ADJ 3 ADJ 5 HYP 4 OPP Army Daniel

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APPLICATIONS: Let’s try a different problem. Sohcahtoa! Army Daniel

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**Check for Understanding.**

Find x given: cos 60° = 0.5 x 60° 1 Army Daniel

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**Check for Understanding.**

Find x given: cos 60° = 0.5 And don’t forget SOH-CAH-TOA x 60° 1 Army Daniel

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Check : ANSWER X = 2 How? x 60° 1 Army Daniel

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**Check : ANSWER How? Use SOH – CAH - TOA cos 60° = .5 = ADJ = 1 HYP x x**

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APPLICATIONS: Let’s try a WORD problem! Sohcahtoa! Army Daniel

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**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!!!] Army Daniel

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**Find the Height of Mt. Sohcahtoa**

What do we know? = 60° Base = 6 miles = 3 miles 2 Height 6 miles Army Daniel

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**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 Army Daniel

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**Which one? Height 6 miles SOH - sin = Opposite side Hypotenuse**

CAH - cos = Adjacent side TOA - tan = Opposite side Adjacent side Height 6 miles Army Daniel

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**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 Army Daniel

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**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 Army Daniel

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**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 Army Daniel

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**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 Army Daniel

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**You deserve a HAND! Now, Let’s Work!!! SOHCAHTOA!!! EXCELLENT!!!**

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**ASSIGNMENT Class Asignment: pp. 356-359 Problems #’s 1 – 40 Homework:**

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

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**Resources Picture of Sohcahtoa:**

[Devil’s Tower] Army Daniel

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Trigonometric Ratios A RATIO is a comparison of two numbers. For example; boys to girls cats : dogs right : wrong. In Trigonometry, the comparison is between.

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