Given triangle ABC with altitude segment AD labeled x. Angles ADB and CDA are 1. by the definition of altitudes, making triangle ABD and triangle CDA right triangles. Using the trigonometric ratios sine of B equals x over c and sine of C equals x over b. Multiplying to isolate x in both equations gives x = 2. and x = b ⋅ sinC. We also know that x = x by the reflexive property. By the substitution property, 3.. Dividing each side of the equation by bc gives: sine of B over b equals sine of C over c.
1. altitudes
2. b ⋅ sinB
3. b ⋅ sinB = c ⋅ sinC

1. right angles
2. b ⋅ sinB
3. b ⋅ sinB =c ⋅ sinB

1. altitudes
2. c ⋅ sinB
3. c ⋅ sinB = b ⋅ sinC

1. right angles
2. c ⋅ sinB
3. c ⋅ sinB = b ⋅ sinC