In triangle ABC, angle C is 90 degrees, AC = 1, BC = √15. Find sine B.

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

AB ^ 2 = AC ^ 2 + BC ^ 2 = 1 + 15 = 16.

AB = 4 cm.

Determine the sine of the angle ABC.

SinABS = AC / AB = 1/4.

Second way.

Let’s define the cotangent of the angle ABC.

CtgBAC = BC / AC = √15 / 1 = √15.

Let’s define the cotangent of the angle ABC through the sine of this angle.

Sin2ABC = 1 / (1 + ctg2ABC) = 1 / (1 + 15) = 1/16.

SinABC = 1/4.

Answer: The sine of the angle ABC is 1/4.