What kind of triangle is called rectangular?
There are several types of triangles. Some have all the angles acute, the other one obtuse and two acute, the third – two sharp and straight. On this basis, each type of these geometric figures and received a name: acute-angled, obtuse-angled and rectangular. That is, rectangle is a triangle whose one angle is 90°. There is another definition, similar to the first. Is called a rectangular triangle whose two sides are perpendicular.
The hypotenuse and the legs
At acute and obtuse triangles to segments connecting the vertices of the angles, referred to as " the parties. From the rectangular triangle the parties have other names. Those that are adjacent to the right angle are called the legs. Side opposite the right angle is called the hypotenuse. In Greek the word "hypotenuse" means "stretched", and "side" - perpendicular.
The ratio between the hypotenuse and the legs of
The sides of a right triangle are linked by defined relationships, which greatly facilitates calculations. For example, knowing the sizes of the other two sides, you can calculate the length of the hypotenuse. This ratio is named opened his math called Pythagorean theorem, and it looks like this:
c2=a2+b2, where C is the hypotenuse, a and b are the legs. That is, the hypotenuse will equal the square root of the sum of the squares of the other two sides. To find any of the sides, enough of the square of the hypotenuse subtract the square of the other leg and removing from the obtained difference square root.
The adjacent and opposite side
Draw a right triangle ACB. Letter C to denote a vertex of a right angle, and the vertices of the acute angles. The side opposite each corner, conveniently called a, b and C, by the names in front of them reclining angles. Consider the angle A. the Leg and for him to be the opposite, side b – yard. The ratio of the opposite leg to the hypotenuse is called the sine. To calculate the trigonometric function by the formula: sinA=a/c. The ratio of adjacent sides to the hypotenuse is called the cosine. It is calculated by the formula: cosA=b/c.
Thus, knowing the angle and one side, you can use the following formulas to calculate the other side. Trigonometric ratios are connected both sides. The ratio of opposite over adjacent to is called the tangent, and adjacent to the opposite – cotangent. To Express these relationships can be a formula tgA=a/b or ctgA=b/a.
