Find the area of the triangle ABC if AB = 5, BC = 7, angle B = 45.

Consider a triangle ABC.

Since, according to the condition of the task, one side AB = 5, and the second BC = 7, and the angle B between these sides is 45 °, then to find the area of this triangle, we will use the formula to find the area through two sides and the angle between them:

S = ½ * a * b * sin b.

Substitute these values into this formula and find the area:

S = ½ * AB * BC * sin B = ½ * 5 * 7 * sin 45 ° = 35/2 * (√2 / 2) = (35√2) / 4.

Answer: the area of the triangle ABC = (35√2) / 4.