In triangle ABC, angle C = 90 degrees, BC = 12 √ 6.cosAB = 30. Find sin B.

The sine of any angle is equal to the ratio of the opposite leg to the hypotenuse. In this case, the hypotenuse (AB) is known, it is equal to 30 cm, and the opposite leg (AC) can be found by the Pythagorean theorem (since the triangle is rectangular). We get:

AB ^ 2 = BC ^ 2 + AC ^ 2;

AC ^ 2 = AB ^ 2 – BC ^ 2;

AC ^ 2 = 30 ^ 2 – (12√6) ^ 2; (We will add 12 under the root)

AC ^ 2 = 900 – (√144 * 6) ^ 2;

AC ^ 2 = 900 – √864 ^ 2;

AC ^ 2 = 900 – 864;

AC = √ (900 – 864);

AC = √36;

AC = 6.

Now we find sin (B):

sin (B) = 6/30 = 1/5.

Or in decimal 0.2.

Answer: sin (B) = 1/5 or in decimal 0.2.