To solve the given problem, we will use trigonometry. We need to find the approximate distance between two persons who are on diametrically opposite sides of a tower. The height of the tower is given as 100 meters, and the angles of elevation to the top of the tower from the two opposite sides are 30° and 60°, respectively.

Let's denote:

• Height of the tower, \(h = 100 \text{ m}\)
• Distance of person A from the base of the tower, \(d_1\), who sees the angle of elevation as 60°
• Distance of person B from the base of the tower, \(d_2\), who sees the angle of elevation as 30°

Using the tangent function for person A, we have:

\(\tan(60^\circ) = \frac{h}{d_1}\)

\(\sqrt{3} = \frac{100}{d_1}\)

\(d_1 = \frac{100}{\sqrt{3}}\)

Rationalizing the denominator:

\(d_1 = \frac{100\sqrt{3}}{3}\)

Using the tangent function for person B, we have:

\(\tan(30^\circ) = \frac{h}{d_2}\)

\(\frac{1}{\sqrt{3}} = \frac{100}{d_2}\)

\(d_2 = 100\sqrt{3}\)

Since the persons are on diametrically opposite sides of the tower, the total distance between them is given by:

\(d_1 + d_2 = \frac{100\sqrt{3}}{3} + 100\sqrt{3}\)

To calculate this, we will bring both terms to a common base:

\(d_1 + d_2 = \frac{100\sqrt{3}}{3} + \frac{300\sqrt{3}}{3}\)

\(d_1 + d_2 = \frac{400\sqrt{3}}{3}\)

Using the approximate value of \(\sqrt{3} \approx 1.732\), we calculate:

\(d_1 + d_2 \approx \frac{400 \times 1.732}{3}\)

\(d_1 + d_2 \approx \frac{692.8}{3}\)

\(d_1 + d_2 \approx 230.9 \text{ m}\)

Hence, the approximate distance between the two persons is 230 m, which matches the given option.