In triangle ABC, angle C is 90∘, AB = 40, AC = 4√51. Find sinA.

1) By the condition of the problem, the triangle is right-angled, therefore, the Pythagorean theorem is applicable to find the side of the BC.

BC ^ 2 + AC ^ 2 = AB ^ 2,

BC = √ (AB ^ 2 – AC ^ 2) = √ (40 ^ 2 – 4√51 ^ 2) = √ (1600 – 816) = √784 = 28.

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

BC / sin A = AB / sin C.

From the formula we have a relation for finding the unknown value sin A:

sin A = BC * sin C / AB.

Since it is known that sin 90 ° = 1, and AB by the problem statement is equal to 40, we obtain that:

sin A = (28 * 1) / 40 = 28/40 = 7/10 = 0.7.

Answer: sin A = 0.7.