SSS theorem illustrates that, if three sides of a triangle are congruent to three corresponding sides of another triangle, the two triangles are congruent.Given the values of 3 sides (a,b,c) we can calculate the values of three angles (A,B,C).
Find angle A,B,C from side a=5 ,side b=6 and side c=7
side a = 5 side b = 6 side c = 7
angle A angle B angle C area perimeter
Substitute the given values in the respective formula,
Let us first find the value of angle A by substituting the values in the formula, A = cos-1(((6 x 6) + (7 x 7) - (5 x 5)) / (2 x 6 x 7)) A = cos-1(.7142) A = 44.4153
Now, find the value of angle B. B = cos-1((5 x 5) + (7 x 7) - (6 x 6)) / (2 x 5 x 7)) B = cos-1(.5428) B = 57.1217
C = cos-1((5 x 5) + (6 x 6) - (7 x 7)) / (2 x 5 x 6)) C = cos-1(.2) C = 78.463
Find the value of S. S = (5+6+7) / 2 S = 9
Area = √9 x (9-5) x (9-6) x (9-7) Area = √216 Area = 14.6969
Now, find the value of perimeter. Perimeter = 5 + 6 + 7 Perimeter = 18