Discussion
A vertical tower stands on ground and is surmounted by a vertical flagpole of height 18 m. At a point on the ground, the angle of elevation of the bottom and the top of the flagpole are 30° and 60° respectively. What is the height of the tower?
Answer: C
Let the tower be \( h \) m and the observer \( d \) m away. The bottom of the flagpole is the top of the tower.
\[ \tan 30^{\circ} = \frac{h}{d} \quad\Longrightarrow\quad d = h\sqrt{3} \]
\[ \tan 60^{\circ} = \frac{h + 18}{d} \quad\Longrightarrow\quad h + 18 = \sqrt{3}\,d = \sqrt{3}\cdot h\sqrt{3} = 3h \]
\[ 2h = 18 \quad\Longrightarrow\quad h = 9 \text{ m} \]
Because \( \tan 60^{\circ} / \tan 30^{\circ} = 3 \), the full height is exactly three times the tower - so the flagpole is twice the tower, and 18 m makes the tower 9 m.
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