The angle of elevation of the top of a tower from a point 20 m away from its base is 45°. What is the height of the tower?

This problem involves trigonometry, specifically the tangent function in a right-angled triangle. The angle of elevation, the height of the tower (opposite side), and the distance from the base (adjacent side) form a right triangle.

• Correct Option B (20 m): We use the formula tan(angle) = Opposite / Adjacent. Given the angle of elevation is 45° and the adjacent side is 20 m, we have tan(45°) = height / 20. Since tan(45°) = 1, it follows that 1 = height / 20, so the height = 20 m.
• Distractor A (10 m): This would be incorrect, perhaps if the angle was different or a division error occurred.
• Distractor C (30 m): This is an arbitrary incorrect value.
• Distractor D (40 m): This would result from multiplying by 2 instead of using the tan(45°) property.