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 pol
Answer: A
Let the pole be \( h \) m and \( d \) the horizontal gap between tower and pole.
From the pole's foot, the 15 m tower top is at \( 60^{\circ} \):
\[ d = \frac{15}{\tan 60^{\circ}} = \frac{15}{\sqrt{3}} = 5\sqrt{3} \approx 8.66 \text{ m} \]
From the pole's top the tower top is only \( 15 - h \) higher, at \( 30^{\circ} \):
\[ 15 - h = d\tan 30^{\circ} = 5\sqrt{3} \times \frac{1}{\sqrt{3}} = 5 \]
\[ h = 10 \text{ m} \]
The shared distance \( d \) is what ties the two sightings together.
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