Knowledge of only one parameter (corner sizes) is not enough for finding of the area of a triangle. If there are any additional sizes, then for determination of the area it is possible to choose one of formulas in which as one of the known variables also corner size is used. Several such formulas applied are most frequent, given below.
Instruction
1. If except the corner size (γ) formed by two parties of a triangle also lengths of these parties are known (A and B), the area (S) of a figure it is possible to define how a half from the work of lengths of the known parties on a sine of this known corner: S=½×A×B×sin(γ).
2. If except the size of one corner (γ), also length of the party (A) adjoining to it and also size of the second corner (β), too adjacent to this party is known, then the area (S) of a triangle can be calculated if to find private from division of the squared length of the only known party into the doubled sum of cotangents of both known corners: S=½×A² / (ctg(γ)+ctg(β)).
3. At the same basic data when in a triangle sizes of two corners are known (γ and β) and length of the party between them (A), it is possible to calculate the area (S) of a figure and a little in a different way. For this purpose it will be required to find the work of the squared length of the known party on sine of both corners, and to divide the received result into the doubled sine of the sum of these corners: S=½×A²×sin (γ)×sin(β)/sin(γ+β).
4. If sizes of all three corners (α, β, γ) in triangle tops are known and also length at least of one of its parties (A), then it is possible to determine the area (S), having calculated fraction in which numerator there will be a work of the squared length of the known party on sine of the corners adjoining to it, and in a denominator - the doubled sine of the angle lying opposite to the known party: S=½×A²×sin (γ)×sin(β)/sin(α).
5. If sizes of all three corners are known (α, β, γ), and there are no data on lengths of the parties, but the radius (R) of the circle described near a triangle is given, then this data set will allow to calculate the area (S) of a figure too. For this purpose it is necessary to double the work of the squared radius on sine of all three corners: S=2×R²×sin (α)×sin (β)×sin(γ).