How to Solve Angle Angle Side Triangle Theorem

Definition:

Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles. Specifying two angles A and B and a side a opposite A uniquely determines a triangle with area.

Example :

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

Given,

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

To Find,

angle C side b side c 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:

b = (5 x sin 7^o)/sin 5^o b = 6.1334

Step 3:

c = (5 x sin 6^o)/sin 5^o c = 5.6525

Step 4:

S = (5+6.1334+5.6525) / 2 S = 8.393 Area = √8.393 x (8.393-5) x (8.393-6.1334) x (8.393-5.6525) Area = √176.3447 Area = 13.2794

Step 5:

Perimeter = 5 + 6.1334 + 5.6525 Perimeter = 16.7859