The angle of elevation of the top of a tower from a point on ground which is 30 mtrs. away from the foot of the tower is 30°. Height of the tower is:?

LohaHridoy
  1. 10/√3 mtrs
  2. 10 × √3 mtrs
  3. 100 mtrs
  4. 20 mtrs

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1 Answers

AhmedNazir

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Option 2 : 10 × √3 mtrs

[ alt="F1 M.G 15.6.20 Pallavi D1" src="//storage.googleapis.com/tb-img/production/20/06/F1_M.G_15.6.20_Pallavi_D1.png" style="width: 164px; height: 148px;">

Given,

The angle of elevation of the top of a tower from a point on ground which is 30 m away from the foot of the tower is 30°.

Formula:

tan θ = Perpendicular/Base

Calculation:

Short Trick:

[ alt="F1 M.G 15.6.20 Pallavi D2" src="//storage.googleapis.com/tb-img/production/20/06/F1_M.G_15.6.20_Pallavi_D2.png" style="width: 163px; height: 155px;">

Ratio of AB : BC = 1 : √3

√3 = 30

⇒ 1 unit = 30/√3

⇒ 1 unit = 10 √3

Detailed solution:

AB is a tower and BC = 30 m.

In ΔABC

tan 30° = AB/BC

⇒ 1/√3 = AB/30

⇒ AB = 30/√3

∴ AB = 10 √3 m

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