A person standing 20 meters away from a wall sees the top of the wall at an angl

A person standing 20 meters away from a wall sees the top of the wall at an angle of elevation of 30 degrees. What is the height of the wall?

A person standing 20 meters away from a wall sees the top of the wall at an angle of elevation of 30 degrees. What is the height of the wall?

Correct Answer: 11.55 meters

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.

Trigonometry – The problem involves using the tangent function to relate the angle of elevation to the height of the wall and the distance from the wall.
Angle of Elevation – Understanding how the angle of elevation from a point to the top of an object can be used to calculate height.
Right Triangle Properties – The scenario can be visualized as a right triangle where the height of the wall is the opposite side, the distance from the wall is the adjacent side, and the angle of elevation is the angle between them.