O (i) (?) Saving... 7. Which of the following is the first step in proving the law of cosines? Use the Pythagorean theorem. Draw a line from one angle in a triangle that is perpendicular to the side across from the angle. Find the cosine of one angle. Find the cosine of two angles.

To prove the law of cosines, the first step is to **draw a line from one angle in a triangle that is perpendicular to the side across from the angle**. Here's a brief explanation of why this is the correct first step: 1. **Understanding the Law of Cosines**: The law of cosines states that for any triangle with sides \(a\), \(b\), and \(c\) opposite to angles \(A\), \(B\), and \(C\) respectively, the relationship is given by: \[ c^2 = a^2 + b^2 - 2ab \cdot \cos(C) \] 2. **Using the Pythagorean Theorem**: While the Pythagorean theorem is related, it applies specifically to right triangles. The law of cosines generalizes this relationship to any triangle. 3. **Drawing a Perpendicular Line**: By dropping a perpendicular from one vertex to the opposite side, you can create two right triangles. This allows you to apply the Pythagorean theorem to these triangles and relate the sides and angles, ultimately leading to the derivation of the law of cosines. Thus, the correct answer is: **Draw a line from one angle in a triangle that is perpendicular to the side across from the angle.**