CDS 2016 PYQ with Answer — Let ABC be a right angled triangle with BC = 5 cm and AC = 12 cm, rig…

2016 · Q46

Let ABC be a right angled triangle with BC = 5 cm and AC = 12 cm, right angled at C. Let D be a point on the hypotenuse AB such that ∠BCD = 30°. What is the length of CD?

Elementary MathematicsGeometry: Lines, Angles and Triangles

A60/13 cm
B17/2 cm
C120{5+122} cm
D120{5+123} cm

Explanation

Note: the options render radicals poorly ('120{5+123}' = 120/(5+12√3)). With ∠BCD = 30° we have ∠ACD = 60°, and CD = AC·BC·sin90°/(AC·sin60°+BC·sin30°) = 60/(6√3+2.5) = 120/(5+12√3) cm (option D).