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How to find side by side and two angles

How to find side by side and two angles

Geometric figure consisting of three points that do not belong to the same straight line called vertices, and three pairs of segments connecting them, called party is called a triangle.

There are many problems on finding the parties andangles of a triangle on a limited number of initial data, one of these problems - finding the side of the triangle on one of its sides, and two angles.

instructions

1

Let constructed triangle ABC and known - side BC and the angles ?? and ??.
It is known that the sum of the angles of any triangle is 180 ?, so the triangle? ABC angle ?? It equals ?? = 180? - (?? + ??).
Find sides AC and AB can be using the sine theorem, which states that
AB / sin ?? = BC / sin ?? = AC / sin ?? = 2 * R, where R - radius described about the triangle ABC circumference?
then we get
R = BC / sin ??,
AB = 2 * R * sin ??,
AC = 2 * R * sin ??.
Sine theorem can be used for any of the two corners and party.

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2

No hand triangle can be found by computing an area under the formula
S = 2 * R? * Sin ?? * Sin ?? * Sin ??,
where R is calculated by the formula
R = BC / sin ??, R - radius of the triangle ABC around here?
Then the side AB can be found by calculating the height lowered on it
h = BC * sin ??,
hence by the formula S = 1/2 * h * AB have
AB = 2 * S / h
Similarly, we can calculate the side AC.

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3

If the external angles of the triangle are given an angle ?? and ??, the inside corners can be found via the corresponding relations
?? = 180? - ??,
?? = 180? - ??,
?? = 180? - (?? + ??).
Next act similarly to the first two points.

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