# How to calculate the angle of inclination

The calculation of the angle of inclination may be needed to solve a variety of problems - the calculation of the slope of the roof, countertops, installing solar panels, antennas, pipes, etc. In addition, the angle of inclination is often necessary to find in the drawing - it may be the slope with respect to a plane tangent angle, etc. Anyway, the search algorithm is the same for any task.

### You will need:

- roulette; - A plumb; - Card; - Level; - Car speedometer; - Calculator.

## Instruction how to calculate the angle of inclination

Step 1:

Try to build a right-angled triangle, mentally, using strips or twine on a pencil drawing - depending on operating conditions. The main thing is that one of the angles of a triangle is equal to 90⁰, and the inclined plane was as hypotenuse, ie the longest side lying opposite the right angle.

Step 2:

If possible, use the pull of the earth - is the easiest way. For example, continue sloping line to the ground or floor, and from the top of the lower twine with a load. Measure the distance between the load and the point of intersection of the oblique line to the ground.

Step 3:

To calculate the angle of inclination of a river or road, determine the height difference at the beginning and end of the object. For example, the highest point lies at an altitude of 100 meters above sea level, and the bottom - at the height of 40 meters (the height difference is determined by the map or leveling). In this example, the vertical leg is equal to 60 meters, and the length of the object is defined by the map or use the direct measurements (road length can be determined by car speedometer).

Step 4:

Transfer the measurement results on a sheet of paper. Schematically picture a triangle to define the size of each side. Divide the length of the vertical leg on the length of the oblique line. The resulting number - the sine of the angle desired. Take a calculator (you can use the calculator online) and by entering the value obtained, press the arcsine (asin). You will get the tilt angle in degrees.

Step 5:

Perhaps you are not able to calculate the length of the sloping sides. In this case, divide the length of the vertical (opposing) leg at the horizontal length (accumbens). You will get the slope, to calculate the angle in degrees, locate it using the arc tangent calculator.

Step 6:

If you are working with a drawing and you need to find the slope of the line, try to determine its equation. Knowing the coordinates of two points, use the formula (x-x1) / (x2-x1) = (y-y1) / (Y1-Y2). Substitute coordinate and bring the equation to the form y = kx + b. The coefficient of x k - the slope of the line. To find the angle, calculate the arc tangent of his.