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Question: Answered & Verified by Expert
$A B C$ is a triangle right-angled at $B$. The hypotenuse $(A C)$ is four times the perpendicular $(B D)$ drawn to it from the opposite vertex and $\mathrm{AD} < \mathrm{DC}$.
What is tan $(A-C)$ equal to?
MathematicsProperties of TrianglesNDANDA 2011 (Phase 1)
Options:
  • A 0
  • B 1
  • C 2
  • D None of these
Solution:
1322 Upvotes Verified Answer
The correct answer is: None of these
$\tan (A-C)=\tan \left(75^{\circ}-15^{\circ}\right)=\tan 60^{\circ}=\sqrt{3}$

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