|
EXAMPLE 14 : A plane is flying from Dallas to Chicago 900 miles away NE. But the pilot decided to fly due north to Topeka instead, then Kansas, and then ENE to Chicago. Find the
actual distance the plane travelled from Dallas to Chicago?
Solution:
From the facts of the data a vector diagram is drawn. From this consider triangle DTC of
the parallelogram.
Now Ð DTC = 1800 - 450 - 22.50 = 112.50
Using the law of sine
Thus the actual distance the plane travelled = DT + TC = 373 + 689 = 1062 miles.
EXAMPLE 15 : Prove the law of cosine using vector method.
Solution:
putting in (1) we get,
a2 = b2 - 2bc cos a +
c2 which is the required one of the laws of cosine.
|
