Question

from the top off a building 60 metre heights the angle of depression of the top and the bottom of a tower are observed at be 30 degree 60 degree respectively find the height of the tower?​

Answer 1

Given :

• From the top of a building 60 m height the angle of depression of the top and the bottom of a tower are observed at be 30° and 60° respectively.

To find :

• Height of the tower.

Solution :

Let the height of the building be AC.

AC = 60 m.

•$\sf{\angle\:FAE=30^\degree}$

•$\sf{\angle\:FAD=60^\degree}$

So,

$\sf{\angle\:FAE=\angle\:AEB=30^\degree\:[Alternate\:angles]}$

$\sf{\angle\:FAD=\angle\:ADC=60^\degree\:[Alternate\:angles]}$

∆ ACD is a right triangle.

$\sf{\frac{AC}{CD}=tan60^\degree}$

$\implies\sf{\frac{60}{DC}=\sqrt{3}}$

$\implies\sf{DC\sqrt{3}=60}$

$\implies\sf{DC=20\sqrt{3}}$

${\boxed{\green{\bold{DC=20\sqrt{3}\:m}}}}$

DC = BE

$\sf{BE=20\sqrt{3}\:m}$

∆ ABE is a right triangle.

$\sf{\frac{AB}{BE}=tan30^\degree}$

$\implies\sf{\frac{AB}{20\sqrt{3}}=\frac{1}{\sqrt{3}}}$

$\implies\sf{AB=20}$

${\boxed{\purple{\bold{AB=20\:m}}}}$

$\sf{BC=AC-AB}\\ \\ \implies\sf{BC=60-20}\\ \\ \implies\sf{BC=40}$

We know,

BC = ED

${\boxed{\blue{\bold{ED=40\:m}}}}$

Hence the height of the tower is 40 m.

Answer 2

$\large\underline\mathrm{Given:-}$

• from the top off a building 60 metre heights the angle of depression of the top and the bottom of a tower are observed at be 30 degree 60 degree respectively.

$\large\underline\mathrm{To \: find}$

• height of the tower

$\large\underline\mathrm{Solution}$

Let the height of the building be AC.

AC = 60m

• FAE = 30°
• FAD = 60°

$\large\underline\mathrm{so,}$

$\implies$FAE = AEB = 30° [Alternate angle]

$\implies$FAD = DC = 60° [Alternate angle]

$\large\underline\mathrm{∆ACD \: is \: a \: right \: triangle}$

$\implies$AC/CD = tan 60°

$\implies$60/DC = √3

$\implies$DC = 60/√3

$\implies$DC = 20√3

$\implies$DC = BC

$\implies$BC = 20√3m

$\large\underline\mathrm{∆ABE \: is \: a \: right \: triangle}$

$\implies$AB/BE = tan 30°

$\implies$AB/20√3 = 1/√3

$\implies$AB = 20m

$\implies$BC = AC - AB

$\implies$BC = 60 - 40

$\implies$BC = 40

$\implies$BC = ED

$\implies$ED = 40m

$\large\underline\mathrm{hence,}$

$\large\underline\mathrm{the \: height \: of \: the \: tower \: is \: 40m.}$

$\large\underline\mathrm{Hope \: it \: helps \: you \: plz \: mark \: me \: brainlist}$