How to find the third party in an isosceles triangle

How to find the third party in an isosceles triangle

It is accepted to call a triangle isosceles in case two of its parties are identical. These parties are designated as "side", and the third – as "basis". It is possible to find basis length in several various ways.


1. To find length of the basis of a triangle at which two parties are equal it is necessary to know radiuses of the entered and described circles, corners and also lengths of sides of a figure. Designate data known to you as follows: α - corners, opposite to the identical parties; β - a corner between the equal parties; R - size of radius of a circumscribed circle; r - size of radius of an inscribed circle.

2. Designate the required party as "x", and known as "y". However, letters can be any (it is possible even to refuse use of symbols of this sort at all, having replaced them, for example, with hearts and circles), the main thing not to get confused and to truly make calculation.

3. Use the formula brought out of the theorem of cosines which says that the square of any party of a triangle is identical to the sum of squares of other two parties with deduction of the doubled work of data of the parties multiplied by a cosine of the angle between them. The formula as follows looks: x=y√2(1-cosβ)

4. If you do not want to use the theorem of cosines, address the theorem of sine, having solved a task by means of such formula: x=2ysin(β/2)

5. If the result seems to you improbable, repeat operation once again. You remember, it is better to check several times right result, than not to notice an error. After all, carrying out necessary calculations requires not much time. Most likely, you will cope with a task for five – six minutes.

6. And the last, be accurate, try to watch not only what you write, but also behind how you do it. Mathematicians often do not pay attention to such trifles as execution of the written decision, as a result they quite often should remake all over again as even a small mistake on the leaf speckled by small badges, to find extremely difficult. Appreciate the work!

Author: «MirrorInfo» Dream Team