options: Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and non-right triangles (e.g., surveying problems, resultant forces).

Prove the Laws of Sines and Cosines and use them to solve problems.
problem_activity: Problem 1
The Law of Cosines states that:
Given
$${\triangle ABC}$$
,
[IMG]
What measurements of a triangle make the most sense to use the Law of Cosines?
Problem 2
For each of the triangles below, would you use the Law of Sines, Law of Cosines, or Pythagorean theorem to find the value of
$$x$$
? Explain your reasoning
[IMG]
[IMG]
[IMG]


correct_option_index: 2