Math, asked by saumya141005, 6 months ago

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

Answers

Answered by bhumi1714
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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