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From a hot air balloon, Sean looks through an angle of depression of 35 degrees to see LeAnn on the on the ground. If Sean and LeAnn are 500 ft. apart by the line of sight distance, to the nearest foot, how far is Sean off the ground?

 Jun 10, 2014

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 #5
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See the picture....Sean is at "A'  about 287 ft off the ground  ....LeAnn is at "B" ...her "horizontal" distance from Sean (CB) is about 410 ft.....the line of sight distance from Sean to LeAnn (AB) is 500 ft.

 Jun 10, 2014
 #1
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So..if you can imagine what we have...The line of sight distance is the hypoteneuse of a right triange. Sean's height off the ground is the adjacent side of an angle that measures (90 - 35) = 55 degrees. So we have

cos(55) = x / 500     where "x" is Sean's height off the ground

500cos(55) = x = about 287 ft.

I can provide a picture.....if you need it.....

 Jun 10, 2014
 #2
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I thought it would be tan?

 Jun 10, 2014
 #3
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No.... the tanget can't be used because we don't know the opposite side (the horizontal distance between Sean and LeAnn if Sean were standing on the ground) or the adjacent side (Sean's height off the ground)

 

 Jun 10, 2014
 #4
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so since i am looking for the adj side the hyp is 500 adj is x and 35 degrees is like him leaning to see her

 Jun 10, 2014
 #5
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+5
Best Answer

See the picture....Sean is at "A'  about 287 ft off the ground  ....LeAnn is at "B" ...her "horizontal" distance from Sean (CB) is about 410 ft.....the line of sight distance from Sean to LeAnn (AB) is 500 ft.

CPhill Jun 10, 2014

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