1316 Trigonometry Law of Sines Chapter 7 Sections 1&2

There is group of formulas that work for most triangles. b a c B C A h

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

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

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

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

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.

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°)

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

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

Use the Law of Sines to find C: 100 67° B A 125 No triangle will be formed with these numbers.

Draw a triangle for each and use the Law of Sines to decide how many triangles are formed B = 47°, b = 4, c = 25 No Triangle C = 60°, b = 30, c = 50 One Triangle 3) B = 20°, a = 12, b = 5 Two triangles 4) B = 37.3°, b = 12.5, c = 20.1 Two triangles 5) A = 102°, a = 5, c = 12 No triangles

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.