How to Solve Side Side Side Triangle Theorem

Definition:

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).

Example :

Find angle A,B,C from side a=5 ,side b=6 and side c=7

Given,

side a = 5 side b = 6 side c = 7

To Find,

angle A angle B angle C area perimeter

Solution:

Substitute the given values in the respective formula,

Step 1:

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

Step 2:

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

Step 3:

Find the value of angle C.

C = cos^-1((5 x 5) + (6 x 6) - (7 x 7)) / (2 x 5 x 6)) C = cos^-1(.2) C = 78.463

Step 4:

Find the value of S. S = (5+6+7) / 2 S = 9

Substitute the values in the area formula,

Area = √9 x (9-5) x (9-6) x (9-7) Area = √216 Area = 14.6969

Step 5:

Now, find the value of perimeter. Perimeter = 5 + 6 + 7 Perimeter = 18