How to Solve Side Angle Side Triangle Theorem

Definition:

Triangles are congruent if any pair of corresponding sides and their included angles are equal in both triangles. Sas of a triangle is calculated with the given values of 2 sides (a,c) and the value of the angle (B).

Example :

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

Given,

side a=5 side c=6 angle A=5^o

To Find,

Angle A, C and side b

Solution:

Substitute the given values in the respective formula,

Step 1:

Let us first find the value of side b by substituting the values in the formula, b = √(5 x 5)+(6 x 6)-(2 x 5 x 6 x cos 5) b = 4.7363

Step 2:

Now, find the value of angle A. A = sin^-1((5 x sin 5)/4.7363) A = sin^-1(.886) A = 53.9681

Step 3:

Calculate the value of angle C. C = sin^-1((6 x sin 5)/4.7363) C = sin^-1(.974) C = 76.319

Step 4:

Find the value of S. S = (5+4.7363+6) / 2 S = 7.8682 Substitute the values in the area formula, Area = √7.8682 x (7.8682-5) x (7.8682-4.7363) x (7.8682-6) Area = √7.8682 x 2.8682 x 3.1319 x 1.8682 Area = √132.432 Area = 11.491

Step 5:

Now, find the value of perimeter. Perimeter = 5 + 4.7363 + 6 Perimeter = 15.7363