In a triangle ABC, the angle is C 90 °, AB is 44, AC is 22√3. find sin A.

In the ABC triangle it is known:

Angle C = 90 °;
AB = 44;
AC = 22√3;
Find sin A.

1) By the Pythagorean theorem, we find the BC leg, since the hypotenuse and the leg are known.

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

BC ^ 2 = AB ^ 2 – AC ^ 2;

BC ^ 2 = 44 ^ 2 – (22√3) ^ 2 = 44 ^ 2 – 22 ^ 2 * 3 = 22 ^ 2 * (2 * 2 – 3) = 22 ^ 2 * 1 = 22 ^ 2;

BC ^ 2 = 22 ^ 2;

BC = 22;

2) Knowing the opposite leg to angle A and the hypotenuse, we find the sine of angle A.

sin A = BC / AB;

Substitute the known values and calculate the value of the sine of angle A. We get:

sin A = 22/44 = 22 / (22 * 2) = 1/2 = 0.5;

Answer: sin A = 0.5.