Question

Please send the answer in structured way , how you solved it ?​

Answer 1

Answer:

M is the image of L in the water so that BL=BM.p is a point at height h above level of water at which the angle of elevation of L is α and the angle of depression of M is β. We have to find BL=x, say.

Let AB=PR=y

LR=ytanα, MR=ytanβ

∴

x−h

x+h

=

ytanα

ytanβ

=

tanα

tanβ

.

Apply comp. and divi.

2h

2x

=

tanβ−tanα

tanβ+tanα

x=h

tanβ−tanα

tanβ+tanα

...(1)

Another form. If we divide above and below of (1) by tanαtanβ, then

x=h

cotβ−cotα

cotβ+cotα

If we change in terms of sin and cos, then from (1)

x=h

sin(β−α)

sin(β−α)