In a right-angled triangle ABC with a right angle C tgB = 4/3. Find sinA.

The tangent of an acute angle of a right-angled triangle is the ratio of the lengths of the opposite leg to the adjacent leg.

Let the length of the leg BC = 3 * X cm, then the length of the leg AC = 4 * X cm.

By the Pythagorean theorem, AB ^ 2 = AC ^ 2 + BC ^ 2 = 16 * X ^ 2 + 9 * X ^ 2 = 25 * X2.

AB = 5 * X cm.

The sine of an acute angle of a right-angled triangle is the ratio of the lengths of the opposite leg to the hypotenuse.

SinA = BC / AB = 3 * X / 5 * X = 3/5.

Answer: The sine of angle A is 3/5.