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SOH-CAH-TOA

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**Warm – up: Find the missing measures. Write all answers in radical form.**

30° 45° x 7 10 z 45° w 60° y

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**The Trigonometric Functions we will be looking at**

SINE COSINE TANGENT

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**The Trigonometric Functions**

SINE COSINE TANGENT

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SINE Prounounced “sign”

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**Prounounced “co-sign”**

COSINE Prounounced “co-sign”

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**Prounounced “tan-gent”**

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**Represents an unknown angle**

Greek Letter q Prounounced “theta” Represents an unknown angle

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hypotenuse hypotenuse opposite opposite adjacent adjacent

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**We need a way to remember all of these ratios…**

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Some Old Hippie Came A Hoppin’ Through Our Old Hippie Apartment

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Sin SOHCAHTOA Opp Hyp Cos Adj Hyp Tan Opp Adj Old Hippie

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Finding SIN, COS, and TAN

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SOHCAHTOA 10 8 6

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**10.8 9 A 6 Find the sine, the cosine, and the tangent of angle A.**

Give a fraction and decimal answer (round to 4 places). 10.8 9 A 6

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**? 5 4 3 Pythagorean Theorem: (3)² + (4)² = c² 5 = c**

Find the values of the three trigonometric functions of . ? Pythagorean Theorem: 5 4 (3)² + (4)² = c² 5 = c 3

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**24.5 8.2 23.1 Find the sine, the cosine, and the tangent of angle A**

Give a fraction and decimal answer (round to 4 decimal places). B 24.5 8.2 A 23.1

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Finding a Side

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**A surveyor is standing 50 feet from the base of a large tree**

A surveyor is standing 50 feet from the base of a large tree. The surveyor measures the angle of elevation to the top of the tree as 71.5°. How tall is the tree? tan 71.5° ? tan 71.5° 71.5° y = 50 (tan 71.5°) 50 y = 50 ( )

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**A person is 200 yards from a river**

A person is 200 yards from a river. Rather than walk directly to the river, the person walks along a straight path to the river’s edge at a 60° angle. How far must the person walk to reach the river’s edge? cos 60° x (cos 60°) = 200 200 60° x x X = 400 yards

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