A person standing 25 meters away from a building observes the top of the building at an angle of elevation of 53 degrees. What is the height of the building?
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A person standing 25 meters away from a building observes the top of the building at an angle of elevation of 53 degrees. What is the height of the building?
Q: A person standing 25 meters away from a building observes the top of the building at an angle of elevation of 53 degrees. What is the height of the building?
Step 1: Understand the problem. You are standing 25 meters away from a building and looking up at the top of the building at an angle of 53 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 you to the building (25 meters), and the angle between the ground and your line of sight to the top of the building is 53 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 building). So, tan(angle) = height / distance.
Step 4: Rearrange the formula to find the height. Height = distance * tan(angle).
Step 5: Plug in the values. Height = 25 meters * tan(53 degrees).
Step 6: Calculate tan(53 degrees). Using a calculator, tan(53 degrees) is approximately 1.327.
Step 7: Multiply the distance by the tangent value. Height = 25 * 1.327.
Step 8: Perform the multiplication. Height ≈ 33.175 meters.
