A man is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?
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A man is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?
Q: A man is standing 30 meters away from a building. If the angle of elevation to the top of the building is 60 degrees, what is the height of the building?
Step 1: Understand the problem. We have a man standing 30 meters away from a building and we need to find the height of the building using the angle of elevation, which is 60 degrees.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building, the other side is the distance from the man to the building (30 meters), and the angle between the ground and the line of sight to the top of the building is 60 degrees.
Step 3: Use the tangent function. In a right triangle, the tangent of an angle is equal to the opposite side (height of the building) divided by the adjacent side (distance from the man to the building). So, tan(60 degrees) = height / 30 meters.
Step 4: Rearrange the formula to find the height. Height = distance * tan(60 degrees).
Step 5: Calculate tan(60 degrees). The value of tan(60 degrees) is √3.
Step 6: Substitute the values into the formula. Height = 30 meters * √3.
Step 7: Simplify the calculation. Height = 30√3 meters.
Step 8: If needed, you can approximate √3 to get a numerical value, but the exact height is 30√3 meters.
