Question

what is sin 23°?
a. $\frac{12}{13}$
b. $\frac{12}{5}$
c. $\frac{5}{13}$
d. $\frac{5}{12}$

Explanation:

Step1: Recall sine - ratio definition

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$.

Step2: Identify opposite and hypotenuse for $\theta = 23^{\circ}$

For the $23^{\circ}$ angle in the given right - triangle, the side opposite to the $23^{\circ}$ angle has length 5 and the hypotenuse has length 13.

Step3: Calculate $\sin23^{\circ}$

$\sin23^{\circ}=\frac{5}{13}$

Answer:

C. $\frac{5}{13}$