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

Let us find the hypotenuse AB according to the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

AB² = AC² + BC²;

AB² = 1² + √15²;

AB² = 1 + 15;

AB² = 16;

AB = √16;

AB = 4.

The sine of the angle in a right-angled triangle is equal to the ratio of the opposite leg to the hypotenuse. This means that the sine of angle B is equal to the ratio of the opposite leg AC to the hypotenuse AB:

sin ∠ B = AC / AB = 1/4 = 0.25.

Answer: 0.25

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