Let's solve the problem in the second image.

Given triangle XYZ:

• Hypotenuse = 35
• One leg (YZ) = 21
• We need to find the other leg (XY) using the Pythagorean Theorem: $a^2 + b^2 = c^2$ $XY^2 + 21^2 = 35^2$ $XY^2 + 441 = 1225$ $XY^2 = 1225 - 441$ $XY^2 = 784$ $XY = \sqrt{784} = 28$

Finding $\tan X$:

$\tan X = \frac{\text{opposite}}{\text{adjacent}} = \frac{21}{28}$

Simplify: $\tan X = \frac{3}{4}$

Final Answer:

$\tan X = \frac{3}{4}$

Would you like a more detailed explanation or have any questions?

Related Questions:

1. How do you determine which side is opposite, adjacent, or the hypotenuse?
2. What are the sine and cosine values for this triangle?
3. How can trigonometric functions be applied to real-world problems?
4. What happens if you accidentally use the hypotenuse as the adjacent side?
5. How can you verify your answer using a calculator?

Tip:

Always check if the fraction can be simplified before submitting your final answer.