Two observers are 100 m apart on level ground with a vertical tower somewhere between them

MATHEMATICS · Single correct · A Level · Mathematics · Trigonometry · Trigonometry

Problem

Two observers are 100 m apart on level ground with a vertical tower somewhere between them. The angles of elevation of the top of the tower from the two observers are 30° and 45° respectively. What is the height of the tower? (a) 50(3+1) m50(\sqrt3+1)\,\text{m} (b) 1003 m\dfrac{100}{\sqrt3}\,\text{m} (c) 50(3−1) m50(\sqrt3-1)\,\text{m} (d) 503 m50\sqrt3\,\text{m}

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