Final answer:
The best time to use trigonometry when solving for a triangle is when you have at least one side length and one angle. Trigonometric ratios and the Pythagorean Theorem are key tools in performing these calculations.
Step-by-step explanation:
Trigonometry is often best utilized when solving for a triangle if you have at least one side length and one angle, which is option 'c'. This is because trigonometric ratios, such as sine, cosine, and tangent, allow you to relate the angles with the sides of a right-angled triangle. For instance, if you are given one angle and the length of the adjacent side, you can use these ratios to solve for other sides or angles of the triangle.
The Pythagorean Theorem, a² + b² = c², another important concept in trigonometry, is independently reliable for calculating the length of the hypotenuse or the sides of a right triangle, provided the other two side lengths are known. This theorem is also the basis for deriving many trigonometric identities.
Using trigonometry, you can effectively solve a wide range of practical problems, such as calculating distances or predicting the result of vector addition when the vectors are at right angles to each other, as stated in the Pythagorean Theorem and related trigonometric principles.