Question

The angle.of depression of the top and bottom of a 7m tall building from the top of a tower is 45° and 60° .Find the of the tower?

Answer 1

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Answer 2

Answer:

Height of tower = 16.56 m

Step-by-step explanation:

Given,

• height of the building = 7 m

• Angle of depression of  top of the building from tower = 45°

• Angle of depression of  top of the building from tower = 60°

Let'x assume that the distance of bottom of the building from tower is R and the height of tower is h.

Then, according to question

  $tan45^0\ =\ \dfrac{h-7}{R}$

=> R = h-7           (1)

and

   $tan60^o\ =\ \dfrac{h}{R}$

$=>\ \sqrt{3}\ =\ \dfrac{h}{R}$

$=>\ R\ =\ \dfrac{h}{\sqrt{3}}$             (2)

From eq. (1) and (2)

$h-7\ =\ \dfrac{h}{\sqrt{3}}$

$=>\ h\ =\ \dfrac{7\sqrt{3}}{\sqrt{3}-1}$

         = 16.56 m

Hence, the height of the tower is 16.56 m.