The tops of two poles of height 25 m and 16 m are connected by a wire. If the wire makes an angle 30° with the vertical, then the distance between the two poles is
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → \(3\sqrt{3}\) m
Draw a horizontal line from B, the top of the 16 m pole, to the taller pole at C. This gives a right triangle ACB: AC is the vertical difference in height and CB is the distance between the poles. The wire AB makes \(30^\circ\) with the vertical AC, so \(\tan30^\circ=\frac{CB}{AC}\).
\(AC=25-16=9\) m
\(\displaystyle d=CB=AC\tan30^\circ=9\times\frac{1}{\sqrt{3}}=\frac{9}{\sqrt{3}}\)
\(\displaystyle \frac{9}{\sqrt{3}}=\frac{9\sqrt{3}}{3}=3\sqrt{3}\) m
Tip: The angle here is measured from the vertical, so the distance is the side opposite it and the height difference the side next to it. Reading it as \(30^\circ\) with the horizontal gives \(9\sqrt{3}\) m, which is Option (1).