PLEASE HELP! LAST PROBLEM! :D A straight road is to be constructed joining two towns A and B. If B is located 44 miles to the west and 30 miles to the south of A, find the length of the road and its bearing from A to B.
The bearing from A to B is
a. S 43 degrees W
b. S 47 degrees W
c. S 56 degrees W
d. S 34 degrees W

Question

PLEASE HELP! LAST PROBLEM! :D A straight road is to be constructed joining two towns A and B. If B is located 44 miles to the west and 30 miles to the south of A, find the length of the road and its bearing from A to B. 
The bearing from A to B is 
a. S 43 degrees W
b. S 47 degrees W
c. S 56 degrees W
d. S 34 degrees W

campbell_st · Answer

draw a diagram

|dw:1343368908956:dw|

to find the length of the road use pythagoras' theorem 

$$x^2 = 44^2 + 30^2$$

solve for x

find the angle theta it will be the size of the angle south of west

$$\tan(\theta) = \frac{30}{44}$$

solve for theta

$$\theta = \tan^{-1}\frac{30}{44}$$

hope this helps