Question

From the top of a minar of height 60m,the top and bottom of a clock tower are observed at the angles of depression of 30 dgree and 60 degree respectively.Then the height of the clock tower in metres is A)40 B)50 C)60 D)80 ​

Answer 1

$\huge{\underline{\underline{\rm{SolutiOn:-}}}}$

${\bf{\red{Given\:that}}}$

• Height of minar = 60m
• Depression angles are 30° & 60° respectively.

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Let AB is minar and EC is tower .

Given, AB = 60 m and EC = ?

In triangle ABC,

Let AB = x

⇒ BD = 60 – x

And, ∠ ACB = ∠OAC (alternate angles are equal)

∠ACB = 30°

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⇒We know that,

tan(theta) = p/b

tan 30° = AB/BC

1/√3=x/BC

BC=x√3............(i)

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⇒In ∆ADE,

∠ADE= ∠OAE(alternate angles are equal)

∠AED=60°

tan60° = AD/DE

√3=60/ DE

⇒DE = 60/√3.............(ii)

∵BC = DE

So, equation (i) = equation (ii)

x√3 = 60/√3

3x = 60

⇒x = 20m.

∵CE = BD and BD = 60 - x

CE = 60 -20

=40m

So, the height of clock tower is 40m.

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