From the triangle in the image:

The given triangle is a right triangle, with one angle $23^\circ$ and the side lengths provided:

• Hypotenuse = $13$,
• Adjacent side to $23^\circ = 12$,
• Opposite side to $23^\circ = 5$.

To find $\sin 23^\circ$:

The sine of an angle in a right triangle is defined as: $\sin \theta = \frac{\text{Opposite side}}{\text{Hypotenuse}}$

For $23^\circ$: $\sin 23^\circ = \frac{\text{Opposite side}}{\text{Hypotenuse}} = \frac{5}{13}.$

So, $\sin 23^\circ = \frac{5}{13} \approx 0.3846.$

Let me know if you'd like further explanations or questions about trigonometry!

Related Questions:

1. How would you calculate $\cos 23^\circ$ in this triangle?
2. What is $\tan 23^\circ$ based on the given triangle?
3. Can you verify if the triangle satisfies the Pythagorean theorem?
4. How is $\sin 67^\circ$ related to $\cos 23^\circ$?
5. How do trigonometric functions change as angles approach $0^\circ$ or $90^\circ$?

Tip:

In right triangles, complementary angles (like $23^\circ$ and $67^\circ$) satisfy the relation $\sin \theta = \cos(90^\circ - \theta)$. Use this property for quick calculations!