Question

according to this diagram, what is sin 23°?
a. \\( \frac { 13 } { 12 } \\)
b. \\( \frac { 5 } { 13 } \\)
c. \\( \frac { 12 } { 13 } \\)
d. \\( \frac { 5 } { 12 } \\)
e. \\( \frac { 12 } { 5 } \\)
f. \\( \frac { 13 } { 5 } \\)

Explanation:

Step1: Recall the definition of sine in a right - triangle

In a right - triangle, \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\).
For \(\theta = 23^{\circ}\), the side opposite to the \(23^{\circ}\) angle is \(5\), and the hypotenuse is \(13\).

Step2: Calculate \(\sin23^{\circ}\)

Using the formula \(\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}\), we substitute the values: \(\sin23^{\circ}=\frac{5}{13}\)

Answer:

B. \(\frac{5}{13}\)