How to Solve Angle Angle Side Triangle Theorem

How to Solve AAS Triangle Theorem - Formula, Example

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.

Formula:

traingle-aas-formula traingle-aas-formula traingle-aas-formula
Example :
aas example

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

Given,

angle A=5o angle B=7o 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 = 18o - 5o - 7o C = 6o

Step 2:

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

Step 3:

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

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