Question 1201089: From a helicopter 1000 ft high, the angles of depression to two islands, in line with, but on opposite sides of the helicopter, are 5.2 degrees and 23.5 degrees. How far apart are the islands? Round to the nearest 100 ft. Choose one of the following options: a) 500 ft b) 1800 ft c) 13,500 ft d) 13,300 ft
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! From a helicopter 1000 ft high, the angles of depression to two islands, in line with, but on opposite sides of the helicopter, are 5.2 degrees and 23.5 degrees. How far apart are the islands?
Round to the nearest 100 ft.
Choose one of the following options: a) 500 ft b) 1800 ft c) 13,500 ft d) 13,300 ft
:
Draw this out, two right triangle sharing a side of 1000 ft
Find the interior angle of the 5.2 degree side: 90-5.2 = 84.8
find the side opposite (s) this angle using the tangent of 84.8
tan(84.8) = s/1000
s = 10988 ft
:
find the interior angle of the 23.5 side: 90-23.5 = 66.5
find the side opposite (s) this angle using the tangent of 66.5
tan(66.5) = s/1000
s = 2300
:
find the distance between the islands: 10988 + 2300 = 13288, opt (d)_
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