If a person standing 15 meters away from a building sees the top of the building at an angle of elevation of 30 degrees, what is the height of the building?
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If a person standing 15 meters away from a building sees the top of the building at an angle of elevation of 30 degrees, what is the height of the building?
Q: If a person standing 15 meters away from a building sees 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. We 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 vertical side we want to find.
Step 3: Recall the definition of 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 person to the building).
Step 4: Write the formula using the tangent function: tan(angle) = opposite/adjacent. Here, tan(30 degrees) = height / 15 meters.
Step 5: Solve for the height of the building. Rearranging the formula gives us height = 15 * tan(30 degrees).
Step 6: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3.
Step 7: Substitute the value of tan(30 degrees) into the height formula: height = 15 * (1/√3).
Step 8: Simplify the expression: height = 15/√3.
Step 9: To make it easier to understand, we can multiply the numerator and denominator by √3: height = (15√3)/(3) = 5√3 meters.
Step 10: Finally, calculate the approximate height: 5√3 meters is about 7.5 meters.
