In triangle ABC, angle C is 90 degrees, AB = 2√13, sin A = 2 / √13. Find the area of the triangle.

1) Using the theorem of sines, the dependence is true:

BC / sin A = AB / sin C.

From the formula we have the relation for finding the unknown side of the aircraft:

BC = AB * sin A / sin C.

Since it is known that sin А = 2 / √13, sin 90 ° = 1, and AB, according to the problem statement, is equal to 2√13, we obtain that the value of the BC side is equal to :.

BC = (2√13 * 2 / √13) / 1 = 4.

2) By the Pythagorean theorem, we find the side of the AC:

AC = √ (AB ^ 2 – AC ^ 2) = √ (2√13 ^ 2- 4 ^ 2) = √ (52 – 16) = √36 = 6.

3) The area of the figure is determined by the formula:

S = 1/2 * BC * AC,

S = 1/2 * 4 * 6 = 12.

Answer: the area of the triangle is 12.