A person is standing 15 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
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A person is standing 15 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
Q: A person is standing 15 meters away from a building. If the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
Step 1: Understand the problem. You have a person standing 15 meters away from a building and looking up at the top of the building at an angle of 30 degrees.
Step 2: Visualize the situation. Imagine a right triangle where one side is the height of the building (which we want to find), the other side is the distance from the person to the building (15 meters), and the angle between the ground and the line of sight to the top of the building is 30 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(30 degrees) = height / 15 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. Now, we can write the equation: height = 15 * tan(30 degrees).
Step 6: Substitute the value of tan(30 degrees) into the equation. This gives us height = 15 * (1/√3).
Step 7: Simplify the equation. This means height = 15/√3 meters.
Step 8: If needed, you can rationalize the denominator. Multiply the numerator and denominator by √3 to get height = 15√3 / 3 meters.
Step 9: Final answer. The height of the building is approximately 15√3 meters.
