https://file.aiquickdraw.com/mathbot/file/1725563264045zo5zctja.jpg

The problem shows a right triangle \( \triangle X Y Z \), with the right angle at \( Y \), and asks for the value of \( \tan X \).

To solve for \( \tan X \), we use the definition of the tangent function:

\[
\tan X = \frac{\text{opposite}}{\text{adjacent}}.
\]

In this case:
- The side opposite angle \( X \) is \( YZ = 48 \).
- The side adjacent to angle \( X \) is \( XY = 14 \).

Thus, we have:
\[
\tan X = \frac{48}{14} = \frac{24}{7}.
\]

Therefore, the correct answer is \( \boxed{\frac{24}{7}} \).

Would you like further explanation on trigonometric functions, or help with another aspect of this problem?

Here are some related questions:
1. What is the sine of angle \( X \) in this triangle?
2. What is the cosine of angle \( X \)?
3. How do you calculate the hypotenuse of a right triangle?
4. How would you find the angle \( X \) using inverse trigonometric functions?
5. How is the Pythagorean theorem applied to this triangle?

**Tip:** For any right triangle, trigonometric ratios can be easily remembered using SOH-CAH-TOA.

Learn how to determine the value of tanX in a right triangle with sides measuring 48 and 14. This step-by-step guide covers the tangent function and trigonometric ratios, suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation