In a right-angled triangle ABC, leg AC = 3 cm, and leg BC = 4 cm.

In a right-angled triangle ABC, leg AC = 3 cm, and leg BC = 4 cm. Calculate the hypotenuse AB, the area of the triangle ABC, the sine and cosine of the angle B?

By the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = BC ^ 2 + AC ^ 2 = 16 + 9 = 25.

AB = 5 cm.

Let’s define the area of the triangle ABC.

Savs = BC * AC / 2 = 4 * 3/2 = 6 cm2.

SinABC = AC / AB = 3/5 = 0.6.

CosABC = BC / AB = 4/5 = 0.8.

Answer: The area of the triangle is 6 cm2, the hypotenuse AB is 5 cm, the sine of angle B is 0.6, the cosine of angle B is 0.8.