A man 40 m from the foot of a tower observes the angle of elevation of the tower to be \(30^\circ\). Determine the height of the tower.

The problem involves finding the height of a tower, given the distance of a person from the foot of the tower and the angle of elevation of the tower from the person. In this case, the person is 40 meters away from the foot of the tower, and observes the angle of elevation to be 30 degrees. To solve for the height of the tower, we can use the tangent function, which relates the opposite (height) and adjacent (distance) sides of a right triangle to the tangent of an angle. Let h be the height of the tower. Then, we have: tangent(30 degrees) = opposite/adjacent tangent(30 degrees) = h/40 Using a calculator, we can evaluate the tangent of 30 degrees to be approximately 0.577. Substituting this value into the equation above, we get: 0.577 = h/40 To solve for h, we can multiply both sides by 40: 0.577 x 40 = h h = 23.08 Therefore, the height of the tower is approximately 23.08 meters. The closest option is 20m, but it's not the correct answer. The correct answer is not given in the options, but it is approximately 23.08 meters, which is between the options 1 and 4.