Step 1: Understand the problem. You have a person standing 20 meters away from a wall and looking up at the top of the wall at an angle of 30 degrees.
Step 2: Identify the right triangle formed by the person, the top of the wall, and the point on the ground directly below the top of the wall.
Step 3: In this triangle, the distance from the person to the wall (20 meters) is the base, the height of the wall is the opposite side, and the angle of elevation (30 degrees) is the angle between the base and the line of sight to the top of the wall.
Step 4: Use the tangent function, which relates the angle to the opposite side (height of the wall) and the adjacent side (distance to the wall). The formula is: tan(angle) = opposite / adjacent.
Step 5: Rearrange the formula to find the height of the wall: height = distance * tan(angle).
Step 6: Substitute the values into the formula: height = 20 * tan(30 degrees).
Step 7: Calculate tan(30 degrees). The value of tan(30 degrees) is 1/√3 or approximately 0.577.
Step 8: Now calculate the height: height = 20 * (1/√3).
Step 9: Simplify the calculation: height = 20 / 1.732, which is approximately 11.55 meters.
