In a right triangle, angle A is one of the acute angles. The side opposite angle A has length 5, and the hypotenuse has length 13. What is…

In a right triangle, the sine of an acute angle is the length of the opposite side divided by the length of the hypotenuse. For angle $A$, the opposite side is 5 and the hypotenuse is 13, so $\sin(A) = \frac{5}{13}$, choice D. The other leg is $\sqrt{13^2 - 5^2} = 12$, so this is a 5-12-13 triangle. Choice A ($\frac{13}{5}$) is the reciprocal, which is cosecant. Choice B ($\frac{12}{13}$) is the cosine of $A$, using the adjacent side. Choice C ($\frac{5}{12}$) is the tangent, opposite over adjacent. Remember SOH-CAH-TOA.