Express tan MM as a fraction in simplest terms.
K
L
M
32
24
40

To express \(\tan M\) as a fraction in simplest terms, we need to interpret the given values as corresponding to a right triangle.

Let's assume \(K\), \(L\), and \(M\) are the angles, and the sides \(32\), \(24\), and \(40\) represent the triangle's side lengths. Since \(M\) is the angle in question, the tangent of \(M\) is given by:

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

From the given values, it seems we have a triangle with sides \(32\), \(24\), and \(40\). Since \(40\) is the largest side, it is likely the hypotenuse. We now need to determine which of the remaining sides (\(32\) or \(24\)) is opposite and which is adjacent to angle \(M\).

Assuming side \(32\) is opposite and side \(24\) is adjacent to angle \(M\):

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

Now, simplify the fraction:

\[
\tan M = \frac{32}{24} = \frac{4}{3}
\]

Thus, \(\tan M = \frac{4}{3}\) in simplest terms.

Would you like more details or have any questions?

Here are 5 related questions:
1. What is \(\sin M\) using the same triangle?
2. How do you calculate \(\cos M\)?
3. How do the angles \(K\) and \(L\) relate in this triangle?
4. How can we verify if this is a right triangle using the Pythagorean theorem?
5. How do you calculate \(\tan M\) for angles in non-right triangles?

**Tip:** Always check if a triangle is right by verifying that the sum of the squares of the two smaller sides equals the square of the hypotenuse!

Express tan M as a fraction in simplest terms. K L M 32 24 40

Learn how to simplify tan M using a right triangle with side lengths of 32, 24, and 40. This trigonometry problem explores key concepts such as the tangent function and right triangle properties. Ideal for students in Grades 9-10.

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