Question #N210
In the figure above, triangle $ABC$ is a right triangle with right angle at $C$. If $AC = 12$ and $BC = 5$, what is the value of $sin A$?
A. $\frac{5}{12}$
B. $\frac{5}{13}$
C. $\frac{12}{13}$
D. $\frac{13}{5}$
Correct Answer is: B
The sine of an angle in a right triangle is equal to the length of the opposite side divided by the length of the hypotenuse. The opposite side to angle $A$ is $BC$, and the hypotenuse is $AB$. Since $ABC$ is a right triangle, we can use the Pythagorean Theorem to find the length of $AB$: $AB^2 = AC^2 + BC^2 = 12^2 + 5^2 = 169$, so $AB = 13$. Therefore, $sin A = \frac{BC}{AB} = \frac{5}{13}$.