In triangle ABC, angle C = 90 degrees, BC = 4, Sin B = 2√6 divided by 5. Find AB.

To solve this task, let’s analyze a right-angled triangle. By the condition of the problem, we know the leg BC and the adjacent angle B. Let us write down what is the hypotenuse in a right-angled triangle through the sine of the angle and the adjacent leg:

sin B = BC / AB;

From this formula, we select the unknown hypotenuse and get the following expression;

AB = BC / sinB;

Substitute the existing values of the leg and sine of the angle into the expression and perform the calculations;

AB = 4 * 5/2 * √6 = 10 / √6;

AB = 5 * √6 / 3;

Answer: hypotenuse AB = 5 * √6 / 3.