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JEE Main202229 Jun 2022Evening ShiftMathematicsHeights and DistancesActual

From the base of a pole of height 20 meter, the angle of elevation of the top of a tower is 60 ° . The pole subtends an angle 30 ° at the top of the tower. Then the height of the tower is:

Options

  1. A15 3
  2. B20 3
  3. C20 + 10 3
  4. D30

Correct answer

D. 30

Step-by-step solution

Plotting the diagram we get, In ∆ A B D tan 60 ° = 20 + y x           . . . i In ∆ A E C tan 30 ° = y x         . . . ii From equation ( i )   &   ( ii ) , ( i )   ( ii )   we get, tan 60 ° tan 30 ° = 20 + y y ⇒ 3 1 / 3 = 20 + y y ⇒ 20 + y y = 3 ⇒ y = 10 So, height of tower = 20 + y = 30   m

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