Class 10

Math

All topics

Some Applications of Trigonometry

A flag-staff of height h stand on the top of a school building. If the angles of elevation of the and bottom of the flag-staff have measure $α$ and $β$ are respectively from a point on the ground, prove that the height of the building is $tanα−tanβhtanβ $

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=$$BDAB $

$BD=ABcotβ$ …………..$(1)$

In $ΔCBD$,

$tanα$ $=BDCB $

$BD=CBcotα[∴CB=CA+AB=h+AB]$

$BD=(h+aB)cotα$ ………$(2)$

Equating $(1)$ & $(2)$ equation,

$ABcotβ=(h+AB)cotα$

$ABcotβ=hcotα+ABcotα$

$AB(cotβ−cotα)=hcotα$

$AB=cotβ−cosαhcotα $

$AB=tanβ⋅tanαtanα−tanβ tanαh $

$AB=h(tanα−tanβtanβ )$,