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