The slope of any line or surface can be found by knowing the trigonometric functions. Whether you need to calculate the angle of a roof, back of a sofa, a pillar, or a straight line on a piece of paper, the methods for determining the angle will be the same.
It is necessary
- - roulette;
- - plumb line;
- - engineering calculator.
To find out the angle of inclination, draw a right-angled triangle, while the inclined line will act as a hypotenuse. To do this, use a plumb line, as it will always create a right angle with the ground. Pick a starting point on your slope or line and use a plumb line and tape measure to measure the distance from that point to the ground (or any other horizontal surface, such as the floor). If there is no plumb line, just grab the weight and hang it on the rope. This distance is called the opposite leg.
Then measure the distance from the point where your plumb line rested to where the incline meets the ground (floor). This will be the adjacent leg. If this distance is difficult to find, instead find the length of the incline from the origin to the ground (floor). This will be the hypotenuse. One way or another, you should have at least two numbers at your disposal - the hypotenuse and one of the legs, or two legs.
If you know the length of the hypotenuse and the length of the opposite leg, calculate the sine (sin) by dividing the length of the leg by the length of the hypotenuse. Now, to find the angle itself, use an engineering calculator to find the arcsin of the resulting number. Please note that in the calculator, its designation can be as follows: sin ^ (- 1) or asin. You will get the angle value in degrees.
If you know the length of the adjacent leg and hypotenuse, find the cosine (cos) by dividing the length of the leg by the length of the hypotenuse. Take a calculator with the arсcos (or acos, or cos ^ -1) button and calculate the inverse cosine, which is the desired tilt angle in degrees.
In order to measure the angle of inclination with known legs, find the tangent (tg). To do this, divide the opposite tangent by the adjacent one. Then, from this number, use a calculator to calculate arctan (it can also be denoted atan or tan ^ -1). The resulting value will be the angle in degrees.