A person standing 20 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

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Q: A person standing 20 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

Solution: Height = distance * tan(angle) = 20 * 1 = 20 meters.

Steps: 8

Step 1: Understand the situation. A person is standing 20 meters away from a building.
Step 2: The person looks up at the top of the building and sees it at an angle of elevation of 45 degrees.
Step 3: Recall that the angle of elevation is the angle between the horizontal line (the ground) and the line of sight to the top of the building.
Step 4: Use the tangent function from trigonometry. The formula is: height = distance * tan(angle).
Step 5: Plug in the values. The distance is 20 meters and the angle is 45 degrees.
Step 6: Calculate tan(45 degrees). The value of tan(45 degrees) is 1.
Step 7: Multiply the distance by the tangent value: height = 20 meters * 1.
Step 8: The result is 20 meters. Therefore, the height of the building is 20 meters.

A person standing 20 meters away from a building observes the top of the building at an angle of elevation of 45 degrees. What is the height of the building?

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