What is cos 16 degrees?

1. Identify the relevant trigonometric ratio: The problem asks for the cosine of an angle in a right-angled triangle. The cosine of an angle in a right-angled triangle is defined as the ratio of the length of the adjacent side to the length of the hypotenuse. This can be remembered by the mnemonic SOH CAH TOA, where CAH stands for Cosine = Adjacent / Hypotenuse.

1. Identify the sides of the triangle: In the given triangle, we are interested in the angle $16^\circ$. The side adjacent to this angle is the side with length 24. The hypotenuse is the side opposite the right angle, which has a length of 25. The side with length 7 is opposite the $16^\circ$ angle.

3. Calculate the cosine: Using the definition of cosine, we have:
$$ \cos(16^\circ) = \frac{\text{Adjacent}}{\text{Hypotenuse}} $$
Substitute the values from the triangle:
$$ \cos(16^\circ) = \frac{24}{25} $$