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Given triangle ABC with altitude labeled x. Angles ADB and CDB are right angles by _____1._____, making triangle ABD and triangle BCD right triangles. Using the trigonometric ratios and . Multiplying to isolate x in both equations gives x = _____2._____ and x = a ⋅ sinC. We also know that x = x by the reflexive property. By the substitution property, _____3._____. Dividing each side of the equation by ac gives: .

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Answer:

(1) ADB = CDB = 90°

(2) c sinA

(3) (sinA)/a = (sinB)/b

Step-by-step explanation:

1. ADB = CDB = 90°

2. c sinA

since,

sin A = x/c , sin C = x/a

so x = c sinA and a sinC

3. from reflective property of x,

since x = c sinA

and x = a sinC

we substitute each equivalently

that is,

c sinA = a sinC

dividing each sides of the equation by ac we have ,

(c sinA)/ac = ( a sinC)/ac

simplifying we have,

(sinA)/a = (sinB)/b

Therefore the above equation is referred to as the SINE RULE.

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