Mathematics, 21.07.2021 06:10 gorillalover9000
I WILL GIVE BRAINLEIST AND POINTS
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 β
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 β
sinB
3. b β
sinB = a β
sinA
1. altitude
2. a β
sinB
3. b β
sinA = a β
sinB
1. right triangle
2. a β
sinB
3. a β
sinA = b β
sinB
1. right triangle
2. b β
sinb
3. b β
sinA = a β
sinB
Answers: 2
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I WILL GIVE BRAINLEIST AND POINTS
Complete the proof of the Law of Sines/Cosines.
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