Find the area of a triangle ABC, if angle A is straight, angle B is 45, hypotenuse BC is 16cm.

The ratio of the adjacent leg to the hypotenuse is the cosine of the angle, which means:

cos B = AB / BC;

AB = BC * cos B = 16 * cos 45 ° = 16 / √2 = 8√2 cm.

The angles of a triangle add up to 180 °. Angle A is a straight line, angle B is 45 °, therefore:

∠С = 180 ° – ∠А – ∠В = 180 ° – 90 ° – 45 ° = 45 °.

Since the two angles of this triangle are equal to each other, then it is isosceles, which means the legs are equal to each other.

The area of a right-angled triangle is equal to half the product of the legs:

S = 0.5 * 8√2 * 8√2 = 64 cm2.