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