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To solve the problem, we need to find \(\cos(\theta)\) for the given right triangle, where \(\theta\) is the angle opposite the side of length 7.

### Step 1: Identify the sides
- **Hypotenuse (c)**: The side opposite the right angle, which is 10.
- **Adjacent side (b)**: The side adjacent to angle \(\theta\), which we need to find \(\cos(\theta)\). This is the side with length 7.

### Step 2: Use the definition of cosine
Cosine of an angle in a right triangle is defined as the ratio of the adjacent side to the hypotenuse:
\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}} = \frac{7}{10}
\]

### Answer:
\[
\cos(\theta) = \frac{7}{10}
\]

This is the exact value, as requested.

Would you like more details or have any questions?

Here are some related questions you might find interesting:
1. How would you find \(\sin(\theta)\) for the same triangle?
2. What is the value of \(\tan(\theta)\) for this triangle?
3. How can the Pythagorean Theorem be used to verify the sides of this triangle?
4. How would you find the value of \(\theta\) in degrees?
5. What is the reciprocal of \(\cos(\theta)\) called and how is it calculated?

**Tip:** When solving trigonometric problems, always ensure you're using the correct side lengths relative to the angle in question.

Find cos(θ) in a right triangle where the adjacent side is 7 and the hypotenuse is 10. Give the exact value.

Solve a trigonometric problem involving the cosine of an angle in a right triangle. Learn how to calculate cos(θ) using the adjacent side (7) and hypotenuse (10) with an exact value. Suitable for students in Grades 9-10.

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