Question

1. find \\(\theta\\).

Explanation:

Identify given values

We have a right triangle.
The side adjacent to \(\theta\) is \(7\).
The hypotenuse is \(10\).

Select trigonometric ratio

We use the cosine ratio.
Recall the cosine formula:

$$\cos(\theta) = \frac{\text{Adjacent}}{\text{Hypotenuse}}$$

Set up equation

Substitute the known values:

$$\cos(\theta) = \frac{7}{10}$$

$$\cos(\theta) = 0.7$$

Solve for theta

Apply the inverse cosine:

$$\theta = \arccos(0.7)$$

$$\theta \approx 45.57^\circ$$

Answer:

\(\theta \approx 45.6^\circ\) (or \(\theta = \arccos(0.7)\))