1. Let's start by understanding the problem: we want to solve a trigonometry problem using cosine. 2. The cosine of an angle in a right triangle is the length of the adjacent side divided by the length of the hypotenuse. This is written as $$\cos(\theta) = \frac{\text{adjacent}}{\text{hypotenuse}}$$. 3. Imagine a triangle where you know the hypotenuse and want to find the adjacent side or the angle. 4. If you want to find the adjacent side, multiply the hypotenuse by the cosine of the angle: $$\text{adjacent} = \cos(\theta) \times \text{hypotenuse}$$. 5. If you want to find the angle, use the inverse cosine function: $$\theta = \cos^{-1}\left(\frac{\text{adjacent}}{\text{hypotenuse}}\right)$$. 6. Let's say the hypotenuse is 10 units and the angle is 60 degrees. 7. Calculate the adjacent side: $$\text{adjacent} = \cos(60^\circ) \times 10 = 0.5 \times 10 = 5$$ units. 8. So, the adjacent side is 5 units long. 9. This is how cosine helps us find sides or angles in triangles. 10. Remember, cosine is just a way to compare the side next to the angle with the longest side in a right triangle. Final answer: The adjacent side length is 5 units when the hypotenuse is 10 units and the angle is 60 degrees.