We are given the triangle
△ABC, with m∠A=60° and m∠C=45°, and AB=8.
To start, we will calculate all angles and sides.
Finding angle B:
The total of all angles in a triangle equals 180.
m∠A + m∠B + m∠C = 180.
Substituting the known values,
60° + m∠B + 45° = 180.
This gives us m∠B = 75°.
Calculating BC:
Using the law of sines,
We can substitute in the values.
Finding AC:
Now we'll input the values.
Calculating Perimeter:
We substitute values here as well.
Calculating Area:
Using the area formula,
we can then insert values.
...............Answer