Question

"In ABC, BC = a = 16, AC = b = 10, and ∠C = 22°. Which equation can you use to find the value of c = AB?

A) ( c = {a^2 + b^2 - 2ab . cos(angle C)} )

B) ( c = {a^2 + b^2 + 2ab . cos(angle C)} )

C) ( c = {a^2 - b^2 + 2ab . cos(angle C)} )

D) ( c = {a^2 - b^2 - 2ab . cos(angle C)} )"

Answer 1

The equation to find the length of side c in triangle ABC, given the sides a and b, and angle C, is the Law of Cosines: c = √{a² + b² - 2ab · cos(angle C)}.

Step-by-step explanation:

To find the length of side c in triangle ABC, we use the Law of Cosines. This law relates the lengths of the sides of a triangle to the cosine of one of its angles. According to the Law of Cosines, the equation to find side c, given sides a and b and the angle C, is c² = a² + b² - 2ab cos(y).

Therefore, with BC = a = 16, AC = b = 10, and ∠C = 22°, the equation to find c = AB is:

A) c = √{a² + b² - 2ab · cos(angle C)}