Question #e7bdd

1 Answer
Oct 26, 2017

~~ 24.0"km"

Explanation:

In the picture, the unknown you are looking for (the distance between the two cities) is unlabeled, but is opposite of the angle of 2.1^o that is shown at the satellite. For convenience sake I will label the angle of 2.1^o as /_C, and the unknown distance between the cities as c. Furthermore, I will arbitrarily label the "top" distance of 370km as a and the "bottom" distance of 350km as b.

In this triangle problem, we have 2 sides (a and b) and the angle between those sides (/_C), and we are solving for the opposite side (c), which means the Law of Cosines is best suited for this problem:

c^2 = a^2 + b^2 -2abcos C

Filling in the knowns as listed above, we have to solve for c, which should be a simple matter so long as care is taken to calculate all values properly. (This is particularly true when using a calculator when some questions may be in radians and others in degrees!)

c^2 = a^2 + b^2 -2abcos C

c^2 = (370)^2 + (350)^2 - 2(370)(350)(cos 2.1)

c^2 ~~ 136900 + 122500 - 259000(0.999)

c^2 ~~ 259400 - 258826.054

c^2 ~~ 573.946

c ~~ sqrt(573.946) ~~ 24.0"km"