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COMEDK2019MathematicsHeights and Distances

-The angle of elevation of the top of a TV tower from three points A, B and C in a straight line through the foot of the tower are , 2 and 3 respectively. If A B=a , then height of the tower is

Options

  1. Aa
  2. Ba
  3. Ca 2
  4. Da 3

Correct answer

C. a 2

Step-by-step solution

Let D E be the height of the tower. Now, in A B E , aligned A E B &= E B C- E A B &=2 - = A E B &= B A E B E &=A B=a aligned Now, E C B=180^ - D C E=180-3 Now, in B E C, B E (180-3 ) = C E 2 [using sine rule] array ll & a 3 = C E 2 & C E= a 2 3 array In E D C , aligned 3 &= D E C E D E &=C E 3 &= a 2 3 3 =a 2 aligned Hence, height of tower is a 2 .

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