Los angeles is 1,744 miles from chicago; chicago is 714 miles from new york; and new york is 2,451 miles from los angeles. The tree cities form a triangle. Find the measure of the angle in the triangle whose vertex represents chicago.

7°

121°

3°

170°

170°

Step-by-step explanation:

Let a be the distance from Los Angeles to Chicago = 1744 miles, b be the distance from Chicago to New York = 714 miles and c be the distance from New York to Los Angeles = 2451 miles.

A is the angle opposite to side a, B is the angle opposite to side b and C is the angle opposite to side c.

Therefore the angle at Chicago is C.

From cosine rule:

c² = a² + b² - 2ab * cos (C)

2ab * cos (C) = a² + b² - c²

cos (C) = (a² + b² - c²) / 2ab

Substituting:

cos (C) = (1744² + 714² - 2451²) / 2*1744*741

cos (C) = - 0.986

C = cos⁻¹ ( - 0.986) = 170°