Triangle? a figure consisting of three points that do not lie on a straight line and three line segments joining these points in pairs.

The points are called vertices (indicated in capital letters), and the segments sides (indicated by small letters) of the triangle.

The following types of triangles: acute triangle (all three angles are sharp), obtuse triangle (one of the angles is obtuse), right-angled triangle (one of the corners line) isosceles (two of its sides equal), equilateral (all its sides are equal).

Find the side of the triangle can be in many ways, but it will always depend on the type of triangle and the initial data.

instructions

1

The ratio of sides and angles in a right triangle:

Let ABC? right-angled triangle, the angle C? straight angles A and B? sharp. Then, according to the definition of cosine: cosine of the angle A is the ratio of the adjacent leg to the hypotenuse BC AB. Sine of angle A is the ratio of the opposite leg to the hypotenuse BC AB. A tangent of an angle is the ratio of the opposite leg to an adjacent BC AC.Iz definitions of data we get the following ratios:

Catete, opposite angle A is equal to the product of the sine of the hypotenuse A, or equal to the product of the second leg at the tangent A-

Catete, adjacent to the angle A is equal to the product of the hypotenuse cosine A-

In a right triangle, either partyIt can be calculated by the Pythagorean theorem, if the other two are known. Pythagorean theorem: in a right triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.

2

Aspect ratio in random triangle:

cosine theorem. The square of any party **triangle** equal to the sum of the squares of the other two parties, without the works of these parties twice the cosine of the angle between them.

sine theorem. hand **triangle** proportional to the sines of the opposite angles.