A measure of the straight line distance between two points

Asked by admin @ in Mathematics viewed by 299 People

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.

Answered by admin @


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 = \frac{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°


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