A geometric figure consisting of three points that do not belong to one straight line called vertices, and three pairs of segments joining them, called sides, is called a triangle.
There are many tasks for finding parties andAngles of a triangle with a limited number of initial data, one of such problems is finding the side of a triangle along one of its sides and two angles.
Let the triangle? ABC be constructed and the side BC and the angles ?? And ??.
It is known that the sum of the angles of any triangle is 180?, So in the triangle? ABC angle ?? Will be equal ?? = 180? - (?? + ??).
Find sides AC and AB can be used using the sine theorem, which reads
AB / sin ?? = BC / sin ?? = AC / sin ?? = 2 * R, where R is the radius of the circle circumscribed about a triangle ABC,
Then we obtain
R = BC / sin ??,
AB = 2 * R * sin ??,
AC = 2 * R * sin ??.
The sine theorem can be applied to any given two angles and Side.
The sides of a given triangle can be found by calculating its area by the formula
S = 2 * R? * Sin ?? * Sin ?? * Sin ??,
Where R is calculated by the formula
R = BC / sin ??, R is the radius of the circumscribed triangle? ABC from here
Then the side AB can be found by calculating the height dropped on it
H = BC * sin ??,
Hence by the formula S = 1/2 * h * AB we have
AB = 2 * S / h
Similarly, you can calculate the AC side.
If the external angles of the triangle are given as angles ?? And ??, then it is possible to find the internal angles by means of the corresponding relations
?? = 180? - ??,
?? = 180? - ??,
?? = 180? - (?? + ??).
Then we proceed similarly to the first two points.