Question

The straight line distance between two cities A and B is 223 km. The straight line distance between cities A and C is 152 km. The straight line distance between cities B and C is 285 km. Find the measure of the angle when standing at city C between the lines of sight to cities A and B.

Answer 1

Angle between the lines of sight to A and B = 50.94°

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 =
`(54600)/(86640)`

CosC = 0.630194

C =
`\text{Cos}^(-1)(0.630194)`

C = 50.94°

Therefore, angle between the lines of sight to cities A and B is 50.94°