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 ⋅ 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