Discussion
The top of a 15 metre high tower makes an angle of elevation of 60° with the bottom of an electronic pole and angle of elevation of 30° with the top of the pole. What is the height of the electric pole?
Answer: D
Let the pole be \( h \) m high and let \( d \) be the horizontal gap between the tower and the pole.
From the pole's foot, the tower top is at \( 60^{\circ} \):
\[ \tan 60^{\circ} = \frac{15}{d} \quad\Longrightarrow\quad d = \frac{15}{\sqrt{3}} = 5\sqrt{3} \approx 8.66 \text{ m} \]
From the pole's top, the tower top is only \( 15 - h \) above, at \( 30^{\circ} \):
\[ \tan 30^{\circ} = \frac{15 - h}{5\sqrt{3}} \quad\Longrightarrow\quad 15 - h = \frac{5\sqrt{3}}{\sqrt{3}} = 5 \]
\[ h = 10 \text{ m} \]
Both sightings share the same \( d \); that is what links the two equations.
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