Question
ABC is a triangular park with AB = AC =100 ~m . A TV tower stands at the mid-point of BC . The angles of elevation of the top of the tower at A, B, C are 45^ , 60^ , 60^ respectively. The height of the tower is
BITSAT
Mathematics
Heights and Distances
2020
BITSAT 2020
BITSAT Mathematics Question (2020) — Solution
Options
- A. 50 ~m
- B. 50 3 ~m
- C. 50 2 ~m
- D. 50(3- 3 ) m
Answer
B. 50 3 ~m
Step-by-step solution
45^ = PQ AQ = h AQ h = AQ Where PQ is tower and ABC is the park, with Q being mid point of the side BC and PQ = h Also, A Q^ 2 +B Q^ 2 =100^ 2 h ^ 2 + h ^ 2 ^ 2 60^ =100^ 2 h ^ 2 [1+ 1 3 ]=100^ 2 h ^ 2 = 3 100^ 2 4 h =50 3
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