UPSC NDA Math Model Paper 3

Given , the top of a hill observed from the top and bottom of a building of height h is at angles of elevation α and β respectively.

From diagram, we have tan‌β=

H

x

and tan‌α=

H−h

x

We have x=

H

tan‌q

So ,tan‌α=

H−h h

tan‌β

⇒tan‌α=

H−h

h

×tan‌β
⇒

tan‌α

tan‌√

=

H−h

h

⇒

tan‌α

tan‌β

=1−

H

h

⇒

H

h

=1−

tan‌α

tan‌β

⇒

H

h

=

tan‌β−tan‌α

tan‌α

⇒H=

h‌cot‌β

cot‌β−cot‌α

The top of a hill observed from the top and bottom of a building of height h is at angles of elevation α and β respectively.
The height of the hill is H=

h‌cot‌β

cot‌β−cot‌α