Question 45
Mathematics
Trigonometric Equations
Hard
Angle of elevation of the top of the tower from 3 points (collinear) A, B and C on a road leading to the foot of the tower are 30° , 45° and 60° respectively. The ratio of AB and BC is
(A) <span class="math-tex">\(\sqrt{3} : 1\)</span>
(B) <span class="math-tex">\(\sqrt{3} : 2\)</span>
(C) 1 : 2
(D) <span class="math-tex">\(2 : \sqrt{3}\)</span>
View Dynamic Solution & Explanation ▼
Correct Solution: Option A
Step-by-step Solution:
Let the tower be PQ, and its height be \( h \), then: \[ AQ = h\sqrt{3} \] \[ BQ = h \] \[ CQ = \frac{h}{\sqrt{3}} \] \[ \Rightarrow \frac{AB}{BC} = \frac{h\sqrt{3} - h}{h - \frac{h}{\sqrt{3}}} = \frac{3 - \sqrt{3}}{\sqrt{3} - 1} = \sqrt{3} \]
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