You will need

- roulette;
- - plumb
- - scientific calculator.

Instruction

1

To find the angle

**of slope**, draw a right triangle, the slant line will act as the hypotenuse. To do this, use the plumb Bob, as it always creates with the ground is a right angle. Choose a starting point on your inclined plane or line, and with the help of a plumb line and measuring tape, measure the distance from that point to the earth (or any other horizontal surface such as the floor). If not plumb, just take the load and hang it on the rope. This distance is called the opposite side.2

Then measure the distance from the point in which you rested your plummet, to the point where inclined surface rests on the ground (floor). This will be the adjacent side over. If this distance is hard to find, instead find the length of the inclined surface from the starting point to the ground (floor). It will be the hypotenuse. Anyway, in your possession should be at least two numbers are the hypotenuse and one leg or two leg.

3

If you know the length of the hypotenuse and the length of the opposite sides, calculate the sine (sin), dividing the length of the leg to the length of the hypotenuse. Now, to find the angle itself, using engineering calculator, find the inverse sine (arcsin) of the obtained number. Notice the calculator symbol may be this: sin^(-1) or asin. You will receive the angle value in degrees.

4

If you are aware of the length of the adjacent sides and the hypotenuse, find the cosine (cos), to do this, divide the length of the leg to the length of the hypotenuse. Take a calculator with a button agso (or acos or cos^-1) and calculate the inverse cosine, which is the desired angle

**of inclination**in degrees.5

To measure the angle

**of inclination**at known legs, find the tangent (tg). To do this, divide the tangent to opposite adjacent. Then from that number using a calculator calculate arctg (it can also be denoted atan or tan^-1). The resulting value will be the size of the angle in degrees.Useful advice

If you have to measure the angle of inclination often enough, purchase a special device - a protractor.

# Advice 2: How to determine the angles of inclination of the plane

In the production of various works on the country or the plot (laying various sites, paving slabs or paths) often have to stitch the oblique tracks site, located on different levels. It is necessary to carefully define and maintain the inclination angles of the plane on such sites.

You will need

- - vertical or horizontal building level;
- - plumb
- - protractor;
- - protractor;
- - smooth wooden beam of length 1.5 m;
- laser level measuring ruler;
- - hydrolevel any marker, peg 2;
- roulette.

Instruction

1

To determine the angle of inclination of the plane the simplest way to use a plumb line, a wooden block and protractor. Put the timber to check the plane. Left hand hold the plumb line at an altitude of 300 – 400 mm. Move the plumb line to the edge of the timber. Reassure the lower part of the slope. The right hand vertically set the protractor with the flat side on the Board. Move the protractor to align the reference point of the protractor with the string of the plumb. Consider the angle of the plane intersection line of the plumb with the scale of the protractor. Get the angle of the plane relative to the vertical. If the desired angle relative to the horizon, calculate it, subtracting from the received angle of 90. This method is use for rough measurements, as it gives a low measurement precision of the angle of inclination of the plane.

2

More specific the following measurement method. Put the timber to check the plane. On the edge of the beam vertically, check the level. Level keep left hand. The right hand attach the protractor to the sides of the angle. On a scale of protractor think of the angle of inclination of the plane.

3

The most accurate method, which used laser level. Install horizontally the base level. Turn on the laser head. Measure the level of elevation from the horizontal of the laser beam to the surface of the plane check on the section length of 1 m. When the value of the differential up to 1 m in this area every of 2.22 cm drop close to 1 degree.

4

High precision of tilt measurement can be achieved using hydrolevel any is a laser level. Measurement hammer parallel to the tilt plane of the two markers at a distance of 1 m. they Mark the horizon with hidrorema. Measure the distance from the labels to the horizon plane. Subtract the larger from the smaller size – get the size of the difference in height at a distance of meters. This value divide by 2.22 and get the angle of the measured area of the plane in degrees.

# Advice 3: How to measure distance in Google

How to find out

**distance**between point A and point on Google map? A painfully familiar question, isn't it? With the help of the map service Google is quite easy to determine the**distance**to a little-known town on the other side of the world or how far from your home is the nearest bus stop.You will need

- Internet access

Instruction

1

Go to Google and click on the word "Map" which is at the top of the search engine.On the right side you will see a map and the left two buttons: "Routes" and "My places". Click on "Routes". Below it will appear two Windows “A” and “b”, that is, the start and end points of reference.Let's say you are in Ufa, and you need to know how much time it will take to get to Perm. In this case the window "And" enter "Ufa" and the window "" - "Perm". Click again on the button under Windows "Routes".The map shows the route, and the Windows “A” and “b” how many miles from one city to another, and also how much time you should spend to reach by car.If you are interested in Hiking, click the button with the image of pedestrian, which is over the Windows “A” and “b”. The service will rebuild the route and automatically calculates

**distance**and expected journey time.2

In the case where it is necessary to measure

**distance**from point “A” to “B”, in one locality, should act according to the above scheme. The difference lies only in the fact that the name of the area you want to add a street and possibly the house number by a comma. ( For example, “A”: Moscow, Tverskaya 5, and V: Moscow, Tsvetnoy Boulevard, 3).3

There are times when you are interested in

**the distance**between the objects "directly": through fields, forests and rivers. In this case, click on the icon toothed ring in the upper corner of the page. In the resulting expanded menu, select "Laboratory Google Maps" and turn on the tool to measure distances, save the changes. In the lower left corner of the map there was a line, click on it. Indicate on the map the starting point, and then endpoint. Between these points on the map a line will appear red and the panel on the left side will show the distance.Useful advice

- you can choose one of the two units of measurement: kilometres or miles;

- clicking on several points on the map, you can determine the distance between multiple points;

- if you access the service using your profile, Google maps will remember your setup in the Laboratory of Google Maps.

- clicking on several points on the map, you can determine the distance between multiple points;

- if you access the service using your profile, Google maps will remember your setup in the Laboratory of Google Maps.

# Advice 4: How to find the tangent of an angle tangent

The geometric meaning of the first order derivative of the function F(x) is a tangent line to its graphics, which passes through a given point of the curve and matching it at this point. Moreover, the value of the derivative at a given point x0 is the slope or tangent of the angle of inclination of the tangent line k = tg a = F`(x0). The calculation of this ratio is one of the most common tasks of the theory of functions.

Instruction

1

Write the given function F(x), e.g. F(x) = (x3 + 15x +26). If the task explicitly specify the point through which the tangent is held, for example, its coordinate x0 = -2, we can dispense with plotting functions and additional straight lines on the Cartesian system OXY. Find the derivative of the first order from the given function F`(x). In this example, F`(x) = (3x2 + 15). Substitute the given value of the argument x0 in the derivative function and calculate its value: F`(-2) = (3(-2)2 + 15) = 27. So you found tg a = 27.

2

When considering tasks where it is required to determine the tangent of the angle of inclination of the tangent to the graph of the function at the point of intersection of this graph with the abscissa axis, you need first to find the numerical value of the coordinates of the point of intersection of the function with OH. For clarity, it is best to build a graph of a function on the two-dimensional plane OXY.

3

Specify the coordinate range for x, for example, from -5 to 5 with step 1. Substituting in the function values x, calculate the corresponding ordinates y and put on the coordinate plane plotting points (x, y). Connect the dots smooth line. You will see the completed chart, the intersection of function and the x-axis. The ordinate of the function at a given point is equal to zero. Find the numerical value of the corresponding argument. For this specified function, for example F(x) = (4x2 - 16), Paranaita to zero. Solve the resulting equation with one variable and calculate x: 4x2 - 16 = 0, x2 = 4, x = 2. Thus, according to the condition of the problem, the tangent of the angle of inclination of the tangent to the graph of the function is to find the point with coordinates x0 = 2.

4

Similarly to the previously described method determine the derivative function: F`(x) = 8*x. Then calculate its value at the point with x0 = 2, which corresponds to the intersection point of the original function with OH. Substitute the obtained value into the derivative function and calculate the tangent of an angle tangent: tg a = F`(2) = 16.

5

When finding the slope at the point of intersection of the function with the ordinate axis (Oh) do the same. Only the coordinate of the initial point x0 should be set to zero.