Question: Find the exact value of csc M in simplest form.
Triangle KML with a right angle at L; side MK is labeled 8, side ML is labeled \sqrt{15}, and side KL is labeled 7.
1. **State the problem:** We need to find the exact value of $\csc M$ in the right triangle $KML$ where $\angle L$ is the right angle.
2. **Identify the sides relative to angle $M$:**
- Hypotenuse: side opposite the right angle, which is $MK = 8$.
- Opposite side to $M$: side $KL = 7$.
- Adjacent side to $M$: side $ML = \sqrt{15}$.
3. **Recall the definition of cosecant:**
$$\csc M = \frac{1}{\sin M} = \frac{\text{hypotenuse}}{\text{opposite side}}$$
4. **Calculate $\csc M$ using the sides:**
$$\csc M = \frac{MK}{KL} = \frac{8}{7}$$
5. **Simplify the fraction if possible:**
$\frac{8}{7}$ is already in simplest form.
**Final answer:**
$$\boxed{\frac{8}{7}}$$