Answer:
(C)
Step-by-step explanation:
It is given that a right triangle, ACB which is right angled at C has BC = 24 inches, and AB = 25 inches.
We know that m∠C=90°,
Using the trigonometry in ΔACB, we have

Substituting the given values, we get
⇒
⇒
⇒
Also, 
Substituting the given values, we get
⇒
⇒
⇒
Therefore, the measure of the angles in triangle ABC are m∠A ≈ 73.7°, m∠B ≈ 16.3°, m∠C ≈ 90°.
Thus, option C is correct.