Given: ΔABC, AB=12, m∠A=60°,m∠C=45°, AB =8 Find the perimeter of ΔABC

The perimeter of ΔABC is 43 units

Step-by-step explanation:

An illustrative diagram is shown in the attachment below.

To find the perimeter of the triangle, we will first determine the length of the unknown sides.

First, we can determine /BC/ using the Sine rule

From Sine rule

∴

In the diagram, and

m∠A=60° and m∠C=45°

∴

To find /AC/, will first determine m∠B

m∠A + m∠B + m∠C = 180° (Sum of angles in a triangle)

60° +m∠B + 45° = 180°

m∠B + 105° = 180°

m∠B = 180° - 105°

m∠B = 75°

Also, using the sine rule

From the diagram,

Now,

The perimeter of ΔABC = /AB/ + /BC/ + /AC/

=

= 43.09 units

≅ 43 units

Hence, the perimeter of ΔABC is 43 units.

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step-by-step explanation: