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).
Find angle C , side a, side b from angle A=5o , angle B=7o and side c=5
angle A=5o angle B=7o side c=5
angle C side a side b area perimeter
Substitute the given values in the respective formula,
C = 18o - 5o - 7o C = 6o
a = (5 x sin 5o)/sin 6o a = 4.4227
b = (5 x sin 7o)/sin 6o
b = 5.4253
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
Perimeter = 5 + 4.4227 + 5.4253 Perimeter = 14.848