In a right-angled triangle ABC with a right angle C, AB = √ 74, sine A 5 / √74. Find AC.

Since angle C is straight, the largest side lies opposite it, which is the hypotenuse. Therefore, AB = √ (74).

The sine of an angle is the ratio of the length of the opposite side to the hypotenuse. This gives us the information that the side opposite the angle A (BC) has a length of 5.

Knowing the 2 sides of a right triangle, we can find the third side using the Pythagorean theorem.

C ^ 2 = A ^ 2 + B ^ 2. We have С = √ (74); A = 5, B = X.
Find X: 74 = 25 + X ^ 2.
X = √ (74 – 25) = √ (49) = 7.

Answer: AC = 7.