Right-angled triangle ABC: angle B = 45 °, side AC 4 cm: find the area ABC.

Let in a right-angled triangle ABC, angle C = 90º, side AB will be the hypotenuse, then, since the angle B = 45 ° and the sum of the angles in the triangle is 180º, we get that angle A = 180º – 90º – 45 °; angle A = 45 °, so the triangle ABC will be isosceles with the base AB. Then the legs CA = CB = 4 cm. The area of the triangle ABC is found by the formula: S = (a • h): 2; substitute the parameters of the triangle: S (Δ ABC) = (CA • CB): 2; S (Δ ABC) = (4 • 4): 2 = 8 (sq. Cm).
Answer: S (Δ ABC) is equal to eight square centimeters.