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Drill Find the missing side length of right triangle ABC. Assume side C is the hypotenuse. 1.A = 7, B = 3 2.A = 9, C = 15

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Section 4.2 Students will calculate trig ratios.

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What is Trig? Based on similar triangles Used to find an unknown angle or side length of a triangle Uses ratios

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Trig Functions A c b B a C The six trig ratios:

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Just Remember: SOH CAH TOA It means: –Sin = opp/hyp –Cos = adj/hyp –Tan = opp/adj

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Find the six trig ratios of angle A in the following right triangle. A 12 B 8 C

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Calculate the six trig ratios of angle A and angle C in the following right triangle. A 4 5 B 3 C

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Special Right Triangles 30-60-90 x√3 2x x 30 60

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Find all sides, then calculate six trig ratios of angle A. A 30 60 B 5 C

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Special Right Triangles 45-45-90 A x x √2 B xC

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Find all sides, then calculate six trig ratios of angle A. 12 A B C

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Use your calculator to calculate: sin 65° cos 125° tan 15° sec 325° csc 230° cot 212°

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Use your calculator to calculate sin cos tan csc sec cot

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Example Let Ө be an acute angle such that sin Ө = 5/6. Evaluate the other five trig functions of Ө.

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Example Let Ө be an acute angle such that sec Ө = 12/5. Evaluate the other five trig functions of Ө.

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Solve the right triangle ABC for all of its unknown parts. A = 20 degrees, a = 12.3 B = 55 degrees, a = 15.58 A = 35 degrees, c = 15 B = 48 degrees, b = 7 C A B

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Evaluate without using a calculator

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Problem Solving with Trig An angle of elevation is the angle through which the eye moves up from horizontal to look at something above. Angle of Elevation

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Problem solving An angle of depression is the angle through which the eye moves down from horizontal to look at something below. Angle of depression

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Example From a point 340 feet away from the base of the Peachtree Center Plaza in Atlanta, Georgia, the angle of elevation to the top of the building is 65 degrees. Find the height of the building.

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Example The angle of depression of a buoy from the top of a lighthouse 130 feet above the surface of the water is 6 degrees. Find the distance from the base of the lighthouse to the buoy.

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Example A tree casts a shadow 51 feet long when the angle of elevation of the sun (measured with the horizon) is 25 degrees. How tall is the tree?

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Homework Read 4.2, do #s 1 – 53 odd, 61, 65

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