The triangle? This is a figure consisting of three points not lying on one line, and three segments connecting these points in pairs.
Points are called vertices (denoted by uppercase letters), and segments are marked by small letters in the triangle.
There are the following types of triangles: An acute triangle (all three angles are sharp), an obtuse triangle (one of the corners is obtuse), a right triangle (one of the corners of a straight line), isosceles (its two sides are equal), equilateral (all its sides are equal).
Find the side of a triangle in different ways, but it will always depend on the type of triangle and the original data.
Aspect ratio and angles in a right-angled triangle:
Suppose that ABC? Right triangle, angle C? Straight, angles A and B? Sharp. Then according to the definition of the cosine: the cosine of the angle A is equal to the ratio of the adjacent BC to the hypotenuse AB. The sine of the angle A is the ratio of the opposing leg BC to the hypotenuse AB. The tangent of the angle A is the ratio of the opposing leg BC to the adjacent AC. From these definitions we obtain the following relations:
The cathetus opposite the corner A is equal to the product of the hypotenuse to the sine A, or is equal to the product of the second leg by the tangent A-
The cathetus adjacent to the corner A is equal to the product of the hypotenuse to the cosine of the A-
In a right-angled triangle, either sideCan be calculated by the Pythagorean theorem, if two others are known. Pythagoras' theorem: in a rectangular triangle the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs.
Aspect ratio in an arbitrary triangle:
The cosine theorem. The square of either side Triangle Is equal to the sum of the squares of the other two sides without the doubled product of these sides by the cosine of the angle between them.
The sine theorem. Parties Triangle Are proportional to the sinuses of the opposite angles.