Calculating the angle of a triangle is a common task in a school geometry course. The way to solve such a problem depends on the conditions known in it. They can be the values of other angles of the triangle, sides, their sines, cosines. You should also pay attention to the shape of the triangle described in the task.
Basic rule
It is worth remembering the most basic rule for all triangles, with which it is customary to start when calculating the angle of a triangle. It sounds like this: the sum of the degree measures of all the angles of a triangle is 180 degrees.
Solutions
Calculating the angles of a right triangle is very simple. In such a triangle, one of the angles is always equal to 90 degrees, respectively, the other two add up to the same amount. If the values of the other two angles are already known in the problem, then you can quickly find the third one by subtracting the sum of the known angles from the sum of the angles of the whole triangle.
You can also calculate the angle of a triangle using the theorem of sines, cosines, tangents and cotangents, knowing any two of its sides,this way:
- the tangent of the angle will be equal to the ratio of the opposite side to the adjacent side;
- sine - the opposite side to the hypotenuse;
- cosine - the ratio of the adjacent side to the hypotenuse.
In the problem, you may also need data on the bisectors and medians of a triangle drawn from an unknown angle.
It should be recalled that the median is the line connecting the corner and the midpoint of the opposite side. A bisector is a line that bisects an angle. Do not confuse them with height and vice versa.
If the median bisects the side opposite the corner, and the resulting angles in the unknown triangle are equal, then this angle is 90 degrees.
If the bisector divides the angle in half, and besides, we know one of the angles of the triangle and the angle belonging to the hypotenuse and the bisector drawn to it, then we can find half of the required angle.
All these rules will help you calculate the angle of a triangle.
