A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?
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A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?
Q: A person standing 40 meters away from a building observes the top of the building at an angle of elevation of 60 degrees. What is the height of the building?
Step 1: Understand the problem. You have a person standing 40 meters away from a building and looking up at the top of the building at an angle of 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 person to the building (40 meters), and the angle of elevation is 60 degrees.
Step 3: Recall 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 person to the building).
Step 4: Write the formula for height. The height of the building can be calculated using the formula: Height = distance * tan(angle).
Step 5: Plug in the values. Here, the distance is 40 meters and the angle is 60 degrees. So, Height = 40 * tan(60°).
Step 6: Calculate tan(60°). The value of tan(60°) is √3.
