UPSC 2017 CDS I Math Paper

Let AB be the height of the aeroplane above the road. Suppose C and D are the positions of the two consecutive kilometer stones on the opposite side of the aeroplane
Here, CD = 1 km In right ΔABC
tan‌α=

AB

BC

⇒BC=

AB

tan‌α

.....(1)
In right ΔABD,
tan‌β=

AB

BD

⇒BD=

AB

tan‌β

......(2)
Adding (1) and (2), we have

AB

tan‌β

+

AB

tan‌α

=BC+BD=CD
⇒AB(

tan‌α+tan‌β

tan‌α‌tan‌β

)=1
⇒AB=

tan‌α‌tan‌β

tan‌α+tanβ