When the elevation of sun changes from 45 to 30 the shadow of a tower increases by 60m then the height of the tower is?


Correct Answer:

D) \( \Large 30 \left(\sqrt{3} + 1\right) m \)


Description for Correct answer:

Let the height of the tower be h.

When the elevation of sun changes from 45 to 30 the shadow of a tower increases by 60m then the height of the tower is?

\( \Large In \triangle BCD, \tan 45 ^{\circ} = \frac{h}{BC} \) => BC = h \( \Large In \triangle ABD, \tan 30 ^{\circ} = \frac{h}{AB} \) => \( \Large AB = \frac{h}{\tan 30 ^{\circ} } \) => \( \Large AB= \sqrt{3}h => AC+BC=\sqrt{3}h \) => \( \Large 60 + h = \sqrt{3}h \) [using (i)]

=> \( \Large h = \frac{60}{\sqrt{3}-1} = \frac{60 \left(\sqrt{3}+1\right) }{2} = 30 \left(\sqrt{3}+1\right) m \)


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11.

An aeroplane flying horizontally at a height of 3 Km, above the ground is observed at a certain point on earth to subtend an angle of 60°. After 15 sec flight, its angle of elevation is changed to 30°. The speed of the aeroplane (taking √3 = 1.732) is

  • 230.63 m/sec

  • 230.93 m/sec

  • 235.85 m/sec

  • 235.85 m/sec

B.

230.93 m/sec

When the elevation of sun changes from 45 to 30 the shadow of a tower increases by 60m then the height of the tower is?
AB = CD = 3000 metreA and C  = Positions of aeroplane

When the elevation of sun changes from 45 to 30 the shadow of a tower increases by 60m then the height of the tower is?

In ΔOAB,

      

When the elevation of sun changes from 45 to 30 the shadow of a tower increases by 60m then the height of the tower is?

When the elevation of sun changes from 45 to 30 the shadow of a tower increases by 60m then the height of the tower is?

In ΔOCD,

When the elevation of sun changes from 45 to 30 the shadow of a tower increases by 60m then the height of the tower is?


When the elevation of sun changes from 45 to 30 the shadow of a tower increases by 60m then the height of the tower is?
∴  Speed of aeroplane

   

When the elevation of sun changes from 45 to 30 the shadow of a tower increases by 60m then the height of the tower is?