Trigonometric leveling

Hello there! Trigonometric leveling is a way of measuring height differences between different points on the ground. It's kind of like playing a game of follow the leader, except instead of people walking through a course, we use math and special tools to follow a straight line between two points.

Let's say we have two points on the ground, Point A and Point B, and we want to figure out how much higher or lower point B is compared to point A. Instead of walking a straight line between the two points, we're going to use math and trigonometry to create an imaginary line. This imaginary line is called a line of sight, and it goes straight from our eyes at point A to an imaginary point on the ground at point B.

To make things simpler, we'll pretend that the ground between points A and B is completely flat with no hills or bumps. This means that the imaginary line of sight will be perfectly straight and won't need to curve to follow the contours of the ground.

Now, we need to measure the angle between the ground and the imaginary line of sight. We do this by using a tool called a theodolite, which looks like a fancy camera on a tripod. The theodolite has a special lens that can measure the vertical angle between two points by using trigonometry.

We start by setting up the theodolite at point A and levelling it so that it's perfectly horizontal. This means that the theodolite won't be tilted in any direction and will be measuring the correct angle.

Next, we look through the lens of the theodolite and line it up with the imaginary point on the ground at point B. The theodolite will then give us a reading of the vertical angle between our eyes at point A and the imaginary point on the ground at point B.

Finally, we use this angle and some more math to figure out the height difference between points A and B. This is called trigonometric leveling because we're using trigonometry to measure the angle and calculate the height difference.

So, to sum it up, trigonometric leveling is a way of measuring height differences between different points on the ground using math and special tools like a theodolite. We use trigonometry to create an imaginary line of sight between two points and measure the angle between this line and the ground. Then, we use this angle and some more math to calculate the height difference between the two points.