Please see the quation in the details as it cannot come in the space provided?

Question

A tower ,h meters high , stands on the top of a mound.At a point on the ground the mound subtends an angle a and the tower an angle b.Show that the height of the mound is (h tan a)/{tan(a+b)-tan a}

Answer 1

let the height of the moundbe x
et thehorizontal dist. bet. theobserver and the mound bey
the equations are
x/y=tan a
x=ytana........(1)

h+x/y=tan(a+b)
h+x=y tan (a+b).....(2)
dividing (1) by (2)
x/h+x=ytana/ytan(a+b)
x tan (a+b)=(h+x) tan a
x tan(a+b)-xtana=h tan a
x=h tan a/[tan(a+b)-tan a]
hence the question

Answer 2

let the height of the mound be l and the distance of the point from the mound x.
then,
tana=l/x
and tanb=(l+h)/x.
so, x=l/tana=(l+h)/tanb.
Solve this for l to get the desired answer.

Answer 3

Look at the end of the book for the answer!