Calculating the angle of a triangle is a common task in school geometry courses. 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. It is also worth paying attention to the type of triangle described in the task.
Basic rule
It is worth recalling the most basic rule for all triangles, from which it is customary to start by calculating the angle of the triangle. It sounds like this: the sum of degree measures of all angles of a triangle is 180 degrees.
Solution options
The calculation of 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 in total give the same. If the values of two other 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 entire 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, thus:
- the tangent of the angle will be equal to the ratio of the opposite side to the adjacent one;
- sinus - of the opposite side to hypotenuse;
- cosine - the ratio of the side to the hypotenuse.
In the problem, you can also find useful 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 middle of the opposite side. Bisector - a line dividing the angle in half. Do not confuse them with height and vice versa.
If the median divides the side of the opposite corner in half, 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 the desired angle.
All these rules will help you calculate the angle of a triangle.