Test Problem (Law of Cosines)?

N

Nick

New member
I took a test yesterday and one of the problems was law of cosines that I wasn't so sure about. Here's the problem.

A boat goes 25 miles due east, then turns 40deg northward for a distance of 30 miles. Calculate the straight line distance of the boat after it's done.

a) 55 (i know that's wrong)
b) 52
c) 50
d) 31 (or something)
e) something even lower than 31 (or something)

by common sense I had ruled out 55 and 31 just seemed to low. And if it's worth mentioning, I answered C =)
 
From your directions ( which are unclear ) will assume ∆ ABC where :-

AB = 25 is horizontal
BC = 30
/_ ABC = 140 °

Using Cosine Rule :-

b ² = 25 ² + 30 ² - 2 ( 25 ) ( 30 ) cos 140 °

b = 42.7 miles
 
Back
Top