Presentation on theme: "1316 Trigonometry Law of Sines Chapter 7 Sections 1&2"— Presentation transcript:
11316 Trigonometry Law of Sines Chapter 7 Sections 1&2
2There is group of formulas that work for most triangles. bacBCAh
3Requirements when using the Law of Sines: You must be given two angles and any side: AAS or ASAORTwo sides and an angle opposite one of them: SSAThe Law of Sines does not work for SSS or SAS
4Find all sides and angles if C = 102.3°, B = 28.7°, and b = 27.4 feet. 27.4 ft102.3°baA49.0°28.7°Bc
5A 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?ba = ?cBCA39°43°shadow98°= 22 ft
6You will get no triangle When you are given two sides and a non-included angle (SSA) – three possibilities existabYou will get no triangleYou will get one triangleabababYou will get two triangles
7Find all angles if A = 85°, a = 15, and b = 25 ft. C25 ftba= 15 ftA85°BcThis does not exist so there is no triangle.
8Find all angles if A = 20.5°, a = 12, and b = 31 feet. C44.3°31 ft94.7 °ba= 12 ft20.5°115.2°A20.5°64.8 °BcThis happens twice on (0°,180°)
9Use the Law of Sines to find B: C8687°BAWith 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
10Use the Law of Sines to find B: C3.5460°BACheck the supplement:The data makes two triangles since both 81.8 & 98.2 work with 60
11Use the Law of Sines to find C: 10067°BA125No triangle will be formed with these numbers.
12Draw a triangle for each and use the Law of Sines to decide how many triangles are formed B = 47°, b = 4, c = No TriangleC = 60°, b = 30, c = 50 One Triangle3) B = 20°, a = 12, b = Two triangles4) B = 37.3°, b = 12.5, c = Two triangles5) A = 102°, a = 5, c = No triangles
13Basic Steps for working with Law of Sines Draw and label a figureUse Law of Sines with the parts you are givenWhen you find an angle (Sin-1) check if the supplement also makes a triangleFind all missing parts that are requested.