question_answer

D and E are two points on the sides AC and BC respectively, of \[\Delta \,ABC\]such that DE = 18 cm, CE = 5 cm and\[\angle DEC=90{}^\circ .\]If \[\tan \,\angle ABC=3.6,\] AC : CD is equal to

A) BC : 2 CE

B) 2 CE : BC

C) 2 BC : CE

D) CE : 2 BC

Correct Answer: A

Solution :

[a] Given, \[\tan \,\angle ABC=3.6\] In \[\Delta DCE,\tan \angle DCE=\frac{18}{5}=3.6\]  \[\therefore \]\[\Delta ABC\] is an isosceles triangle where \[AB=AC\] Now, drawing \[AM\bot BC\] \[DE\parallel AM,\] \[\therefore \]In \[\Delta ACM\]and \[\Delta DCE\] \[\frac{AC}{CD}=\frac{MC}{CE}=\frac{\frac{1}{2}BC}{CE}=\frac{BC}{2CE}\]