The triangle which has two parties, equal on length, is called isosceles. These parties are considered as side, and a third call the basis. One of important properties of an isosceles triangle: corners, opposite to its equal parties, are equal among themselves.
It is required to you
- - Bradis's tables;
- - calculator;
- - ruler.
Instruction
1. Designate the parties and corners of an isosceles triangle. Let the basis will be b, a side, corners between side and the basis α, a corner, opposite to the basis β, h height.
2. Find side by means of Pythagorean theorem which says that the square of a hypotenuse of a rectangular triangle is equal to the sum of squares of legs – с^2= а^2+b^2. If at an isosceles triangle besides the basis height is known, then on properties of an isosceles triangle it is its median and divides a geometrical figure into two equal rectangular triangles.
3. Substitute the necessary values in the equation. So, in this case it will turn out: а^2 = (b/2) ^2+h^2. Solve the equation: and = √ (b/2) ^2+h^2. In other words, the side is equal to the square root taken from the sum of a half of the basis squared, and bar which is cleared also in a square.
4. If an isosceles triangle – rectangular, corners at its basis are equal 45 °. Count the side size by means of the theorem of sine: a/sin 45 ° = to b/sin 90 ° where b is the basis, and – side, sin 90 ° is equal to unit. As a result it turns out: = b*sin 45 ° = b * √ 2/2. That is, the side is equal to the basis increased by a root from two, divided into two.
5. Use the theorem of sine also when an isosceles triangle not rectangular. On the basis and a corner, adjacent to it, α find side: = b*sinα/sinβ. β calculate a corner by means of property of triangles which says that the sum of all corners of a triangle is equal 180 °: β = 180 ° - 2*α.
6. Apply the theorem of cosines according to which the square of the party of a triangle is equal to the sum of squares of two other parties minus the doubled work of data of the parties increased by a cosine of the angle between them. In relation to an isosceles triangle the given formula looks thus: = b/2cosα.