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Two observers stand on opposite sides of a vertical tower. From one point, the angle of elevation of the top is 45°, and from the other point it is 30°. If the tower is 40 m tall, what is the distance between the two observers?

1. 40 m
2. 40√3 m
3. 68.280 m
4. 109.28 m

Correct answer: 109.28 m

Solution

Using trigonometric relationships, the height of the tower and the angles of elevation allow us to calculate the distances from each observer to the base of the tower. By applying the tangent function for both angles and solving the resulting equations, we find the total distance between the two observers to be approximately 109.28 m.

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