Towers and antennas are often some of the tallest structures on the visible landscape, especially in rural areas. Calculating the height of these towers and antennas is relatively easy using basic trigonometric calculations if you know your distance to the tower or antenna and the angle at which your eyesight makes a line with the top of the tower, relative to the ground.
Measure your distance from the base of the antenna or tower, using a tape measure. Generally, the farther away you are, the more accurate your calculation will be.
Measure the angle of your line of sight to the top of the tower relative to the ground. To do this, tie one end of the string to the center of a protractor and the other end to a small weight. The weight will be pulled down by gravity and will therefore be at a 90-degree angle with the ground. The tower or antenna you are attempting to measure will likely be at this same 90-degree angle, so the string will be parallel to the tower.
Lying on the ground so your line-of-sight begins as low to the ground as possible, hold the zero-degree end of the protractor up to your eye and point the 180-degree end at the top of the tower so that if you are looking along the flat underside of the protractor with the arched side facing the ground, you can just barely see the top of the tower over the end of the protractor.
Without moving the string, grasp it where it touches the rounded edge of the protractor and record the angle measurement at this point. This is the angle of your line of sight with the ground.
Use trigonometry to calculate the height of the tower. The tower, the ground between you and the tower and your line of sight to the top of the tower form the three sides of a right triangle. Because of this, you can use trigonometry and a scientific calculator to find the height of the tower.
From Step 2, you have the angle formed by your line of sight and the ground. You also have the distance from you to the base of the tower, the length of one of the triangle's sides.
Now, simply use the scientific calculator to find the tangent of the angle you found in Step 2 and multiply this number by the distance you are standing from the tower. This will give you an indirect measurement of the height of the tower.