A vertical pole 27 feet tall stands on a hillside that makes an angle of 19o with the horizontal. Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 80 feet downhill from the base of the pole. Round answer to two decimal places.

Question

anonymous · Answer

these are the options:	
 
92.39 feet
 
 B.	
 
100.82 feet
 
 C.	
 
84.02 feet
 
 D.	
 
89.62 feet
 
 E.	
 
75.65 feet

anonymous · Answer

92.39 feet

We will need to use the law of cosines.  I think the tough part is the meaning of 19 degrees with the horizon; this means the angle is 

109 = 90 + 19

Using the law of cosines we have

c^2 = 80^2 + 27^2 - 2(80)(27)cos(109)

and taking the square root of both sides we have

c = 92.39 feet

anonymous · Answer

Thank you so much! :)