How to Solve Angle Side Angle Triangle Theorem

Definition:

Triangles are congruent if any two angles and their included side are equal in both triangles. Given the values of 2 angles (A,B) and the value of the side (c) that is in between those 2 angles we can calculate the values of the remaining 1 angle (C) , 2 sides(a,b).

Example :

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

Given,

angle A=5^o angle B=7^o side c=5

To Find,

angle C side a side b area perimeter

Solution:

Substitute the given values in the respective formula,

Step 1:

C = 18^o - 5^o - 7^o C = 6^o

Step 2:

a = (5 x sin 5^o)/sin 6^o a = 4.4227

Step 3:

b = (5 x sin 7^o)/sin 6^o

b = 5.4253

Step 4:

S = (5+4.4227+5.4253) / 2

S = 7.424

Area = √7.424 x (7.424-5) x (7.424-4.4227) x (7.424-5.4253)

Area = √17.9512 Area = 1.39

Step 5:

Perimeter = 5 + 4.4227 + 5.4253 Perimeter = 14.848