Question

the angle of elevation of a cloud from a two point distance 's' and 't' from its feet are complementary. Prove that hight of tower is under root st.

Answer 1

Solution.

Let, the height of the tower be h. (AB)
AD and AC are the distances from the cloud inclined at a angle (Theta) and (90°-Theta) respectively.
BC=t and BD = s

In the triangleABC,
perendicular=AB=h
and base=BC=t
tan (90°-Theta) = AB/BC
cot theta = h/t.......eq (1)

Now in triangleABD,
perpendicular = AB= h
And base = BD = s

tan theta= AB/BD
= h/s.............eq (2.)

Multiply eq (1.) and eq (2.)
cot Theta × tan Theta = h/t×h/s
1/tan Theta × tan Theta = h^/st
1 = h^/st
st = h^ ( where ^ stands 2.)

h =
$\sqrt{st}$
Therefore, height of the cloud Underoot st.
Hence, Proved.

Hope this will help you.

Answer 2

Let the height of cloud be x.

Therefore, the height of cloud is ${\sqrt{st}}$

$\underline{\mathfrak{\huge{Thank\: You.}}}$