Proof: Cosine 2a
Let's prove the following theorem:
if ∠ABC is a right angle, then cosine of (m∠CAB) = (distance BA) / (distance AC)
Proof:
Given
1 | ∠ABC is a right angle |
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# | Claim | Reason |
---|---|---|
1 | cosine of (m∠CAB) = (distance BA) / (distance CA) | if ∠ABC is a right angle, then cosine of (m∠CAB) = (distance BA) / (distance CA) |
2 | distance CA = distance AC | distance CA = distance AC |
3 | (distance BA) / (distance CA) = (distance BA) / (distance AC) | if distance CA = distance AC, then (distance BA) / (distance CA) = (distance BA) / (distance AC) |
4 | cosine of (m∠CAB) = (distance BA) / (distance AC) | if cosine of (m∠CAB) = (distance BA) / (distance CA) and (distance BA) / (distance CA) = (distance BA) / (distance AC), then cosine of (m∠CAB) = (distance BA) / (distance AC) |
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