Question

the angle of elevation from a point 300feet from the base of a pole of height h as the level ground to the top of the pole is 45 the equation can be used to find the height of the pole is​

Answer 1

Step-by-step explanation:

Let AB be the tower and (A, B)

the flag staff, CA=hm

Let D be observation point, such that angle of elevation of top & c bottom, be α & β respectively.

In ΔABD,

tanβ=

BD

AB

BD=ABcotβ …………..(1)

In ΔCBD,

tanα =

BD

CB

BD=CBcotα[∴CB=CA+AB=h+AB]

BD=(h+aB)cotα ………(2)

Equating (1) & (2) equation,

ABcotβ=(h+AB)cotα

ABcotβ=hcotα+ABcotα

AB(cotβ−cotα)=hcotα

AB=

cotβ−cosα

hcotα

AB=

tanβ⋅tanα

tanα−tanβ

tanα

h

AB=h(

tanα−tanβ

tanβ

),