Geometry is the study of shapes and figures that take up a given space. Geometric problems try to identify the size and scope of those shapes by solving mathematic equations. In a geometry problem there are two types of information "givens" and "unknowns." The givens, represent the information in the problem that is given to you. The unknowns are the pieces of the equation you must solve. It is possible to find the area of a triangle with only one side length given. However, to solve the problem, you also need to know two of the interior angles.
Determine the third angle of the triangle. For example, the sample problem has a triangle where side B is 10 units. Both angle A and Angle B are 50 degrees. Solve for angle C. Math law states that the angles of a triangle add up to 180 degrees, therefore Angle A + Angle B + Angle C = 180.
Insert the given angles into the equation.
50 + 50 + C = 180
Solve for C by adding the first two angles and subtracting from 180.
180 - 100 = 80
Angle C is 80 degrees.
Use the sine rule to re-write the equation.. The sine rule is a mathematical rule that aids in solving unknown angles and lengths. The sine rule states:
a/sin A = b/sin B = c/sin C
In the equation the small a, b and c represent the lengths, while the capital A, B and C represent the sides of the triangle. Because all portions of the equation equal each other, you can use any two portions. Use the portion for the side you were given. In the sample problem this is side B, 10 units.
Following the laws of math re-write the equation as:
c = b sin C / sin B
The small c represents the side you are solving for. The capital C is moved to the numerator on the opposite side of the equation because according to the laws of math you must isolate c in order to solve for it. When moving a denominator, it goes to the numerator so it can be later multiplied.
Insert the givens into your new equation.
c = 10 sin 100 / sin 50
Place this into your geometry calculator to return a result of:
c = 12.86
Solve for the area of the triangle. To find the area of a triangle you need two side lengths which you have now obtained. The equation for the area of a triangle is A = 1/2 b x h. The "b" represents base and the "h" represents height.
A = 10 x 12.86
A = 128.60 units^2 (squared)