Question

The angles of elevation of the top of a tower from two points distant s and t from its foot are complementary. Then the height of the tower is ____________.

पर्याय

• st

• `"s"^2 "t"^2`

• `sqrt"st"`

• s/t

Answer 1

The angles of elevation of the top of a tower from two points distant s and t from its foot are complementary. Then the height of the tower is `underline(sqrt"st")`.

Explanation:

Let the height of the tower be h.

Construct figure according to given information as

`"tan" theta = "AC"/"BC"`

`=> "tan" theta = "h"/"s"` .... (i)

`"tan" (90 - theta) = "AC"/"PC"`

`=> "cot" theta = "h"/"t"` ..... (ii)

Multiplying euations (i) and (ii), we get

`"tan" theta xx "cot" theta = "h"/"s" xx "h"/"t"`

`=> 1 = "h"^2/"st"`

`=> "h" = sqrt"st"`