In triangle ABC, angle C is 90 degrees BC = 8√6 sinB = 0.2 find the length of the sides AB.

Triangle ABC is rectangular with 90 ° right angle.

Since BC = 8 * √6 and sin b = 0.2, then we find the side AB.

To calculate the hypotenuse AB of the ABC triangle, we use the formula:

cos b = BC / AB;

We multiply the values cross by cross and then we get:

BC = AB * cos b;

AB = BC / cos b;

AB = BC / √ (1 – sin ^ 2 b);

Substitute the known values into the formula and calculate the leg of the triangle ABC.

AB = 8 * √6 / √ (1 – 0.2 ^ 2) = 8 * √6 / (1 – 0.04) = 8 * √6 / √0.96 = √ (6 / 0.96) * 8 = √ (1 / 0.16) * 8 = 8 / √0.16 = 8 / 0.4 = 80/4 = 20;

Answer: AB = 20.