Question

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

NCERT Class X
Mathematics - Mathematics

Chapter _SOME APPLICATIONS OF
TRIGONOMETRY

Answer 1

Given the angle of elevation of the top of a tower from a point on a ground = 30⁰.
The distance between the point and foot of the tower is 30m.
Now ,Let it's height be 'x'.
We know that Tan θ = opposite side/adjacent side
                     Tan 30⁰= x/30
                       1/√3 = x/30
                         x√3 = 30
                           x = 30/√3 = 10 √3m.
                              

Answer 2

Diagram are given below 
In right ΔABC, AB = the heught of the tower. The point C is 30 m away from the foot of the tower,
 Therefore,    AC = 30 m
 Now,           AB/AC =tan 30°
 ⇒               h/30 = 1/√3              (tan 30°= 1/√3)
 ⇒               h = 30/√3 = 30/√3×√3/√3  = 10√3
  Thus,required height of the tower is 10√3 m.
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