UPSC NDA Math Model Paper 1

Consider, AB and CD are two pillars. AB=16m and CD=9m
The distance between two pillars of length 16 metres and 9 metres is x metres.
From given data, we havetan θ=

CD

BD

=

9

x

tan‌α=

AB

BD

=

16

x

Given, the two angles of elevation of their respective tops from the bottom of the other are complementary to each other
tan‌α×tan‌θ=1
⇒

16

x

×

9

x

=1
⇒x=12
The distance between the two pillars of length 16 metres and 9 metres is x metres. If the two angles of elevation of their respective tops from the bottom of the other are complementary to each other, then the value of x(in metre) is = 12