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**1316 Trigonometry Law of Sines Chapter 7 Sections 1&2**

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**There is group of formulas that work for most triangles.**

b a c B C A h

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**Requirements when using the Law of Sines:**

You must be given two angles and any side: AAS or ASA OR Two sides and an angle opposite one of them: SSA The Law of Sines does not work for SSS or SAS

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**Find all sides and angles if C = 102.3°, B = 28.7°, and b = 27.4 feet.**

27.4 ft 102.3° b a A 49.0° 28.7° B c

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**A pole tilts toward the sun at an angle of 8°**

A pole tilts toward the sun at an angle of 8°. If it casts a 22 foot shadow and the angle of elevation from the tip of the shadow to the top of the pole is 43°, how tall is the pole? b a = ? c B C A 39° 43° shadow 98° = 22 ft

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**You will get no triangle**

When you are given two sides and a non-included angle (SSA) – three possibilities exist a b You will get no triangle You will get one triangle a b a b a b You will get two triangles

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**Find all angles if A = 85°, a = 15, and b = 25 ft.**

C 25 ft b a = 15 ft A 85° B c This does not exist so there is no triangle.

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**Find all angles if A = 20.5°, a = 12, and b = 31 feet.**

C 44.3° 31 ft 94.7 ° b a = 12 ft 20.5° 115.2° A 20.5° 64.8 ° B c This happens twice on (0°,180°)

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**Use the Law of Sines to find B:**

C 8 6 87° B A With Sine there may be an angle in Quad II that also works so you must check the supplement: This is too large to be a triangle with the 87 given

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**Use the Law of Sines to find B:**

C 3.5 4 60° B A Check the supplement: The data makes two triangles since both 81.8 & 98.2 work with 60

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**Use the Law of Sines to find C:**

100 67° B A 125 No triangle will be formed with these numbers.

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**Draw a triangle for each and use the Law of Sines to decide how many triangles are formed**

B = 47°, b = 4, c = No Triangle C = 60°, b = 30, c = 50 One Triangle 3) B = 20°, a = 12, b = Two triangles 4) B = 37.3°, b = 12.5, c = Two triangles 5) A = 102°, a = 5, c = No triangles

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**Basic Steps for working with Law of Sines**

Draw and label a figure Use Law of Sines with the parts you are given When you find an angle (Sin-1) check if the supplement also makes a triangle Find all missing parts that are requested.

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MM4A6c: Apply the law of sines and the law of cosines.

MM4A6c: Apply the law of sines and the law of cosines.

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