Two women and lie on the leveled ground at opposite sides of 150 m tall tower. If A observes the top of the tower at an angle of 60° and B observes the same point at an angle of 30°, then how far the two women can be away from each other?

To find out how far the two women can be away from each other, we can use trigonometry and the concept of similar triangles based on the angles given in the problem.

1. Let's consider the triangles formed by the tower and the lines of sight of A and B. We have two right triangles, one for each woman's observation:

- Triangle for A: 60° angle at the top of the tower

- Triangle for B: 30° angle at the top of the tower

2. For triangle A, we can use the tangent function to calculate the distance from A to the tower:

tan(60°) = tower height / distance from A to the tower

tan(60°) = 150 / x, where x is the distance from A to the tower

x = 150 / tan(60°)

3. For triangle B, we can also use the tangent function to calculate the distance from B to the tower:

tan(30°) = tower height / distance from B to the tower

tan(30°) = 150 / y, where y is the distance from B to the tower

y = 150 / tan(30°)

4. To find the total distance between the two women, we add the distances from A and B to the tower:

Total distance = x + y

5. Calculate x and y using the values of the tangents of 60° and 30°:

x = 150 / tan(60°) ≈ 150 / 1.732 ≈ 86.60 m

y = 150 / tan(30°) ≈ 150 / 0.577 ≈ 259.81 m

6. Finally, calculate the total distance:

Total distance = 86.60 m + 259.81 m ≈ 346.41 m

Therefore, the two women can be approximately 346.41 meters away from each other.