Question
From the top of a cliff 50 m high, the angles of depression of the top and bottom of a tower are observed to be 30^ and 45^ . The height of tower is
BITSAT
Mathematics
Heights and Distances
2024
BITSAT 2024 (Memory Based Paper 3)
BITSAT Mathematics Question (2024) — Solution
Options
- A. 50 m
- B. 50 3 ~m
- C. 50( 3 -1) m
- D. 50 (1- 3 3 ) m
Answer
D. 50 (1- 3 3 ) m
Step-by-step solution
Accoding to condition, Let, height of tower =h In A B D, 45^ = A B B D B D=50 ~m Now, In A C C^ aligned & & 30^ & = A C^ C^ C \\ & & 1 3 & = 50-h 50 \\ & & 50 & =50 3 -h 3 \\ & & h 3 & =50( 3 -1) \\ & & h & =50 (1- 1 3 ) \\ & & & =50 (1- 3 3 ) m aligned
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