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We are given a right triangle \( \triangle FHG \), and the goal is to find the cosine of angle \( \angle F \).

### Cosine Definition:
In a right triangle, the cosine of an angle is defined as:

\[
\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}
\]

For \( \angle F \), the adjacent side is \( FH \) and the hypotenuse is \( FG \).

### Information from the diagram:
- \( FG = 53 \) (hypotenuse)
- \( FH = 45 \) (adjacent side)

Thus, the cosine of \( \angle F \) is:

\[
\cos(F) = \frac{FH}{FG} = \frac{45}{53}
\]

This fraction is already in its simplest form.

### Final Answer:
\[
\cos(F) = \frac{45}{53}
\]

Would you like further clarification or more details?

Here are 5 related questions:
1. How can you calculate the sine of \( \angle F \) using the given triangle?
2. What is the tangent of \( \angle F \) in this triangle?
3. How do you find the length of side \( HG \) using the Pythagorean theorem?
4. What are the basic trigonometric ratios for a right triangle?
5. How would you solve for \( \angle G \) using trigonometry?

**Tip:** When working with right triangles, the Pythagorean theorem and trigonometric ratios are essential tools to determine unknown sides or angles.

Find the cosine of ∠F in the triangle with hypotenuse FG = 53 and adjacent side FH = 45.

Learn how to find the cosine of angle F in a right triangle where the hypotenuse is 53 units, and the adjacent side is 45 units. This problem covers key trigonometric concepts and is suitable for students in Grades 8-10.

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