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The problem involves a right triangle with side lengths 7, 24, and 25. We are asked to find the trigonometric ratios \(\cos \theta\), \(\sin \theta\), and \(\tan \theta\) using these side lengths.

### Given:
- Hypotenuse (\(c\)) = 25
- Opposite side to \(\theta\) (\(a\)) = 7
- Adjacent side to \(\theta\) (\(b\)) = 24

### To find:
- \(\cos \theta\)
- \(\sin \theta\)
- \(\tan \theta\)

### Formulas:
1. \(\sin \theta = \frac{\text{Opposite}}{\text{Hypotenuse}} = \frac{a}{c} = \frac{7}{25}\)
2. \(\cos \theta = \frac{\text{Adjacent}}{\text{Hypotenuse}} = \frac{b}{c} = \frac{24}{25}\)
3. \(\tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{a}{b} = \frac{7}{24}\)

### Solutions:
- \(\sin \theta = \frac{7}{25}\)
- \(\cos \theta = \frac{24}{25}\)
- \(\tan \theta = \frac{7}{24}\)

Would you like more details on how these ratios were calculated or any other related information?

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Here are 5 additional questions to expand your understanding:

1. How do you determine which side is opposite or adjacent in a right triangle?
2. What are the other trigonometric ratios (cosecant, secant, and cotangent) for this angle?
3. How can you use the Pythagorean theorem to verify that this triangle is a right triangle?
4. How would the trigonometric ratios change if the angle \(\theta\) was at the other non-right angle?
5. What are the possible angles \(\theta\) for this right triangle?

**Tip:** Always remember that the sum of the angles in any triangle is 180 degrees, and in a right triangle, one angle is always 90 degrees.

A right triangle has side lengths 7, 24, and 25. Use these lengths to find cos θ, sin θ, and tan θ.

Calculate the trigonometric ratios cos θ, sin θ, and tan θ for a right triangle with side lengths 7, 24, and 25. This problem demonstrates key trigonometric concepts and the use of the Pythagorean Theorem. Ideal for students in Grades 8-10.

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