Question

Find the area of the triangle ABC given angle A = 45°, b = 8, and c = √2.

Answer 1

The Triangle can be represented from the given figure with angle A = 45
and b= 8 and c= √2
Now, Draw a perpendicular from CD on AB, here CD is the Height(h) of the Triangle and AB(b) is the Base
In ΔACD, CD= h = √2sin45 = √2/√2 = 1

so

=>ar(ABC) = b×h/2

=>Area = 8 × 1/2
=>Area = 4 unit square

Answer 2

In the attachment I have answered this problem.

I applied the formula 1/2 bc Sin A from trigonometry to find the area of the triangle.

I hope this answer helps you