In triangle ABC, angle C is 90, tgA = √3. find sinВ

The tangent of the angle of a right-angled triangle is the ratio of the opposite leg to the adjacent leg, then:

tgBAC = BC / AC = √3 / 1.

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

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

AB ^ 2 = AC ^ 2 + BC ^ 2 = X ^ 2 + 3 * X ^ 2 = 4 * X ^ 2.

AB = 2 * X cm.

Determine the sine of the angle ABC of a right-angled triangle ABC,

SinABS = AC / AB = X / 2 * X = 1/2 = 0.5.

Answer: The sine of angle B is 0.5.