Final answer:
To find the area of triangle ABC, use the formula for the area of a triangle: Area = 1/2 * base * height. Calculate the height using the sine function and the Pythagorean theorem. Substitute the values to find the area of the triangle.
Step-by-step explanation:
To find the area of the triangle ABC, we can use the formula for the area of a triangle: Area = 1/2 * base * height. In this case, the base is represented by side b, which has a length of 8, and the height can be found using the Pythagorean theorem. Given that angle A is 45° and side c is √2, we can use the sine function to find the height: height = c * sin(A). Substituting the values, we get: height = √2 * sin(45°) = √2 * 1/√2 = 1. Now we can calculate the area: Area = 1/2 * 8 * 1 = 4 square units.