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

Solution:

A = 45°, b = 8, and c = √2 [Given]

The formula to find the area of the triangle is

A = ½ × b × c × sin A

Substituting the given values

A = ½ × 8 × √2 × sin 45°

By further calculation

A = ½ × 8 × √2 × 1/√2

So we get

A = 4 unit²

Therefore, the area of the triangle is 4 unit².

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

Summary:

The area of the triangle ABC given angle A = 45°, b = 8, and c = √2 is 4 unit².