A man is standing 25 meters away from a vertical pole. If he looks up at an angl

A man is standing 25 meters away from a vertical pole. If he looks up at an angle of 45 degrees, what is the height of the pole?

A man is standing 25 meters away from a vertical pole. If he looks up at an angle of 45 degrees, what is the height of the pole?

Correct Answer: 25 meters

Step 1: Understand that the man is looking up at a pole from a distance of 25 meters.
Step 2: Recognize that the angle of 45 degrees means that the height of the pole and the distance from the man to the pole are equal.
Step 3: Use the tangent function, which relates the angle to the opposite side (height of the pole) and the adjacent side (distance from the man to the pole).
Step 4: Calculate the height of the pole using the formula: Height = distance * tan(angle).
Step 5: Since tan(45 degrees) equals 1, the calculation becomes Height = 25 meters * 1.
Step 6: Conclude that the height of the pole is 25 meters.

Trigonometry – The problem involves using the tangent function to relate the height of the pole to the distance from the pole and the angle of elevation.
Angle of Elevation – Understanding that the angle of elevation from the man's line of sight to the top of the pole is crucial for applying the tangent function correctly.