A person is standing 15 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?
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A person is standing 15 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?
Q: A person is standing 15 meters away from a vertical pole. If the angle of elevation to the top of the pole is 60 degrees, what is the height of the pole?
Step 1: Understand the problem. You have a person standing 15 meters away from a vertical pole and looking up at the top of the pole.
Step 2: Identify the angle of elevation. The angle of elevation to the top of the pole is 60 degrees.
Step 3: Visualize the situation. Imagine a right triangle where one side is the height of the pole, the other side is the distance from the person to the pole (15 meters), and the angle between the ground and the line of sight to the top of the pole is 60 degrees.
Step 4: Use the tangent function. In a right triangle, the tangent of an angle is the opposite side (height of the pole) divided by the adjacent side (distance from the pole). So, tan(60 degrees) = height / 15 meters.
Step 5: Rearrange the formula to find the height. Height = distance * tan(60 degrees).
Step 6: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 7: Substitute the values into the formula. Height = 15 meters * √3.
Step 8: Simplify the expression. The height of the pole is 15√3 meters.
