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riosd920
riosd920
20.09.2020 • 
Mathematics

(05.04 MC) Complete the proof of the Law of Sines/Cosines. Triangle ABC with side a between points B and C, side b between points A and C. Segment drawn from point C to point D where D is between points A and B, segment CD is labeled x. Given triangle ABC with 1. segment CD labeled x. Angles ADC and CDB are right angles by the definition of altitudes, making triangle ADC and triangle BCD right triangles. Using the trigonometric ratios sine of A equals x over b and sine of B equals x over a. Multiplying to isolate x in both equations gives x = b ⋅ sinA and 2.. We also know that x = x by the reflexive property. By the substitution property, 3.. Dividing each side of the equation by ab gives: sine of A over a equals sine of B over b. 1. altitude 2. b ⋅ sinB 3. b ⋅ sinB = a ⋅ sinA 1. altitude 2. a ⋅ sinB 3. b ⋅ sinA = a ⋅ sinB 1. right triangle 2. a ⋅ sinB 3. a ⋅ sinA = b ⋅ sinB 1. right triangle 2. b ⋅ sinb 3. b ⋅ sinA = a ⋅ sinB

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