Question

A triangle has sides x, y, and z. xA) cos⁻¹(x²-y²-z²-2yz)

B) cos⁻¹(z²-y²-x²-2xy)
C) cos⁻¹(-(z²-y²-x²)/(2xy))
D) cos⁻¹(-(x²-y²-z²)/(2yz))
E) cos⁻¹(-(x²+y²-z²)/(2yz))

Answer 1

The correct answer is E) cos⁻¹(-(x²+y²-z²)/(2yz)). This answer can be derived by applying the Law of Cosines and using the given expression in the answer choice.

Step-by-step explanation:

The correct answer is E) cos⁻¹(-(x²+y²-z²)/(2yz)).

This answer can be derived by applying the Law of Cosines, which states that in a triangle with sides of lengths x, y, and z, the cosine of one of the angles, denoted as C, can be found using the following formula:

cos(C) = (x² + y² - z²) / (2xy)

In this case, the given expression in the answer choice corresponds to the cosine of angle C, which aligns with the Law of Cosines. Therefore, option E is the correct answer.