Question

The angles of elevation of the top of a tower, as seen from two points A and B situated in the same line and at distance x and y respectively. from the foot of the tower, are complementary. Find the height of the tower. ​

Answer 1

√xy is the correct one

Step-by-step explanation:

Let the angle of elevation made at a distance of x= α

Then, angle of elevation made at a distance of y= 90−α

Let the height of tower = h

Then, tan∠ of elevation =

distance

Height

Thus, tanα=

x

h

tan(90−α)=

y

h

or cotα=

y

h

Multiply both the equations,

tanαcotα=

x

h

.

y

h

→

xy

h

2

=1

Or, h

2

=xy

h=

xy