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Published byDerek Cox Modified over 7 years ago

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Use Pythagorean Theorem: x = 12.68 = 12.7 rounded This is a 30-60-90 Triangle: ON A SHEET OF PAPER

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Right Triangle Trigonometry Mr. Miller Standard addressed: Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent.

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VERY IMPORTANT: YOU MUST SET YOUR CALCULATOR TO DEGREE Press Mode key Set to DEGREE

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All Scientific Calculators have a DEGREE or DEG setting Make sure you know how to set your personal calculator. If you need help let Mr. Miller know Click here to use Online Calculator

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Adjacent Opposite Side Hypotenuse of a Right Angle Triangle. Terms you need to be familiar with!!!

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Adjacent side Opposite side Hypotenuse This is the Greek letter Theta. It is used to represent an unknown angle.

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Hypotenuse Adjacent side Opposite side

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Naming Sides of Right Triangles

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Warm – up: Find the missing measures. Write all answers in radical form. 45° x w 7 60° 30° 10 y z Session 17

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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

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Prounounced “tan-gent” TANGENT

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Prounounced “theta” Greek Letter Represents an unknown angle

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Sin, Cos, Tan Buttons Sine, Cosine, Tangent These are the three basic Trig ratios (fractions) used to solve for sides and angles in right triangles.

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opposite hypotenuse adjacent hypotenuse opposite adjacent

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We need a way to remember all of these ratios…

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

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SOH CAH TOA Old Hippie Sin Opp Hyp Cos Adj Hyp Tan Opp Adj

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Finding sin, cos, and tan

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Table of Trigonometric Ratios Solve for x: Sin 18 = x Cos x =.6157 Tan 76 = x ◦ ◦ ◦ x =.3090 x = 52 ◦ x = 4.0108

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Definition of Sine Ratio.Sine Ratio For any right-angled triangle Sin = Opposite side Hypotenuse (SOH)(SOH)

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A B C 15 8 Find the sine of A and B 17

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6 8 10 SOH CAH TOA

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Find the sine, the cosine, and the tangent of angle A. Give a fraction and decimal answer (round to 4 places). 9 6 10.8 A

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

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Find the sine, the cosine, and the tangent of angle A A 24.5 23.1 8.2 B Give a fraction and decimal answer (round to 4 decimal places).

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Finding a side

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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? 50 71.5° ? tan 71.5° y = 50 (tan 71.5°) y = 50 (2.98868) Ex.

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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? 200 x Ex. 5 60° cos 60° x (cos 60°) = 200 x X = 400 yards

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Now you know three ways to find parts of a right triangle: 1.Pythagorean Theorem – If you know two sides, then use to find the third side. 2.Special Right Triangles- If it is a 30-60-90 or 45-45-90, then follow the pattern to find the side lengths. 3.Right Triangle Trigonometry- Use Sin, Cos, and Tan (Soh Cah Toa) ratios to solve for sides and angles of a right triangle.

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HOMEWORK Complete the 7.3 Packet

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