Thank you for the correction. Let's revisit the problem with the correct side lengths:

- The side opposite to \(M\) is \(KL\), which has a length of \(32\).
- The side adjacent to \(M\) is \(ML\), which has a length of \(24\).

Now, we calculate \(\tan M\) using the formula:

\[
\tan M = \frac{\text{opposite side to } M}{\text{adjacent side to } M}
\]

\[
\tan M = \frac{KL}{ML} = \frac{32}{24}
\]

Next, we simplify \(\frac{32}{24}\):

\[
\frac{32}{24} = \frac{32 \div 8}{24 \div 8} = \frac{4}{3}
\]

So, the correct answer is:

\[
\tan M = \frac{4}{3}
\]

Do you need more details or have any questions about this solution? 

Here are 8 related questions for practice:

1. How would you find \(\tan L\) in this triangle?
2. What is the sine of angle \(M\) in this triangle?
3. What is the cosine of angle \(M\) in this triangle?
4. How do you calculate the hypotenuse \(MK\) using the Pythagorean theorem?
5. If angle \(M\) is 45 degrees, what would \(\tan M\) be?
6. How would you verify the simplification of \(\frac{32}{24}\)?
7. What would \(\tan M\) be if the side lengths of the triangle were doubled?
8. What is the relationship between \(\tan M\), \(\sin M\), and \(\cos M\)?

**Tip:** When solving trigonometric problems, double-check that you’ve correctly identified the opposite, adjacent, and hypotenuse sides for the angle in question.

Learn how to calculate the tangent of angle M in a right triangle where KL is 32 and ML is 24. Step-by-step solution using trigonometric ratios. Suitable for high school students.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation