Answer:
Angle between the lines of sight to A and B = 50.94°
Step-by-step explanation:
Distance between the cities A and B = 223 km
Distance between the cities B and C = 285 km
Distance between the cities A and C = 152 km
By applying cosine rule in triangle ABC,
AB² = AC² + BC² - 2(AC)(BC)CosC
(223)² = (152)² + (285)² - 2(152)(285)CosC
49729 = 23104 + 81225 - (86640)CosC
CosC = [tex]\frac{54600}{86640}[/tex]
CosC = 0.630194
C = [tex]\text{Cos}^{-1}(0.630194)[/tex]
C = 50.94°
Therefore, angle between the lines of sight to cities A and B is 50.94°
