A person standing 50 meters away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
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A person standing 50 meters away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
Q: A person standing 50 meters away from a building observes the top of the building at an angle of elevation of 30 degrees. What is the height of the building?
Step 1: Understand the problem. A person is standing 50 meters away from a building and sees the top of the building at an angle of elevation of 30 degrees.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building (opposite side), the other side is the distance from the person to the building (adjacent side), and the angle is 30 degrees.
Step 3: Use the tangent function. The tangent of an angle in a right triangle is the ratio of the opposite side (height of the building) to the adjacent side (distance from the person to the building). So, tan(30 degrees) = height / 50 meters.
Step 4: Find the value of tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 5: Set up the equation. Replace tan(30 degrees) in the equation: height = 50 * tan(30 degrees). This becomes height = 50 * (1/√3).
Step 6: Calculate the height. Multiply 50 by (1/√3) to get height = 50/√3.
Step 7: Simplify the height. You can also express this as height = 15√3 meters by rationalizing the denominator.
