CDS 2018 PYQ with Answer — ABC is a right angled triangle with base BC and height AB. The hypote…

2018 · Q64

ABC is a right angled triangle with base BC and height AB. The hypotenuse AC is four times the length of the perpendicular drawn to it from the opposite vertex. What is tan C equal to?

Elementary MathematicsTrigonometry

A2 - √3
B√3 - 1
C2 + √3
D√3 + 1

Explanation

The perpendicular from B to the hypotenuse has length AB·BC/AC (equating area formulas), so AC = 4·AB·BC/AC gives AC² = 4·AB·BC. With tanC = AB/BC = t, Pythagoras gives 1 + t² = 4t, i.e. t = 2 ± √3. Since BC is named the 'base' (the longer leg), tanC = AB/BC < 1, selecting 2 − √3, option (A). (This matches embibe's worked solution of the same question.)