Proof: Tangent 5
Let's prove the following theorem:
if ∠ABC is a right angle, then tangent of (m∠CAB) = (distance CB) / (distance AB)
Proof:
Given
1 | ∠ABC is a right angle |
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# | Claim | Reason |
---|---|---|
1 | tangent of (m∠CAB) = (distance BC) / (distance AB) | if ∠ABC is a right angle, then tangent of (m∠CAB) = (distance BC) / (distance AB) |
2 | distance BC = distance CB | distance BC = distance CB |
3 | (distance BC) / (distance AB) = (distance CB) / (distance AB) | if distance BC = distance CB, then (distance BC) / (distance AB) = (distance CB) / (distance AB) |
4 | tangent of (m∠CAB) = (distance CB) / (distance AB) | if tangent of (m∠CAB) = (distance BC) / (distance AB) and (distance BC) / (distance AB) = (distance CB) / (distance AB), then tangent of (m∠CAB) = (distance CB) / (distance AB) |
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