If the hypotenuse of a right triangle measures 10 units and the length of the opposite side is 6 units, what is the value of the cosecant of the angle opposite the 6-unit side?

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To find the cosecant ($$\csc$$) of the angle opposite the 6-unit side in a right triangle, follow these steps:

1. **Identify the Sides:**
   - **Opposite side ($$a$$)**: 6 units
   - **Hypotenuse ($$c$$)**: 10 units

2. **Recall the Definition of Cosecant:**
   $$
   \csc(\theta) = \frac{1}{\sin(\theta)} = \frac{\text{Hypotenuse}}{\text{Opposite side}}
   $$

3. **Apply the Values:**
   $$
   \csc(\theta) = \frac{10}{6} = \frac{5}{3}
   $$

So, the value of the cosecant of the angle opposite the 6-unit side is:

$$\boxed{\dfrac{5}{3}}$$
The cosecant of the angle is $$\frac{5}{3}$$.

If the hypotenuse of a right triangle measures 10 units and the length of the opposite side is 6 units, what is the value of the cosecant of the angle opposite the 6-unit side?

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