If a person is standing 15 meters away from a building and the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
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If a person is standing 15 meters away from a building and the angle of elevation to the top of the building is 30 degrees, what is the height of the building?
Q: If a person is standing 15 meters away from a building and 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: Identify the right triangle formed by the person, the top of the building, and the base of the building. The distance from the person to the building is the base (15 meters), and the height of the building is the opposite side.
Step 3: Use the tangent function, which relates the angle of elevation to the opposite side (height of the building) and the adjacent side (distance from the building). The formula is: tan(angle) = opposite/adjacent.
Step 4: Plug in the values into the formula. Here, angle = 30 degrees, opposite = height of the building, and adjacent = 15 meters. So, tan(30) = height / 15.
Step 5: Calculate tan(30). The value of tan(30 degrees) is 1/√3.
Step 6: Set up the equation: 1/√3 = height / 15.
Step 7: Solve for height by multiplying both sides by 15: height = 15 * (1/√3).
Step 8: Simplify the expression: height = 15/√3.
Step 9: To make it easier to understand, you can multiply the numerator and denominator by √3: height = (15√3)/3 = 5√3 meters.
Step 10: If you want a decimal approximation, calculate 5√3, which is approximately 7.5 meters.
