Question

a vertical tower stands on a horizontal plane and is surmounted by a vertical flag staff of height h . At a height on the plane ,the angle of elevation of the bottom and the top of the flag staff are
$\alpha$
and
$\beta$
respectively. Prove that the height of the tower is h tan a

​

Answer 1

Answer:

Let height be y ΔOAC

tanθ=

B

P

tanβ=

OA

CA

tanβ=

x

y+h (y+h)→ Let AB, AB+BC

Let OA→ x

x=[

tanβ

y+x

]

Consider ΔOAB

tanα=

x

y

=

Base

perpendicular

x=

tanα

y

tanα

y

=

tanβ

y+h

ytanβ=tanαy+tanαh

ytanβ−tany=tanαh

y(tanβ−tanα)=tanαh

y=

tanβ−tanα

htanα

This proved.

Step-by-step explanation:

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