SOLUTION: A worm is 14m from the bottom of a tree. It sees a squirrel on the tree at an angle of elevation of 22 degree. It also sees a bird on the tree at an angle of elevation of 55 degree

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Question 315945: A worm is 14m from the bottom of a tree. It sees a squirrel on the tree at an angle of elevation of 22 degree. It also sees a bird on the tree at an angle of elevation of 55 degree. How far is the squirrel from the bird?
Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

Do worms have eyes?  I don't think so, but I think they can detect
light.  But detecting squirrels and birds and their angles of elevation?
I dunno!  :-)



The worm is at point W, the squirrel is at point S, and the bird 
is at point B.  The base of the tree is point X.

WE want to find SB, the distance from the squirrel to the bird.

WX = 14

We use the smaller (red) right triangle SWX to find SX

SX%2FWX=SX%2F14=opp%2Fadj=tan%28%2222%B0%22%29

SX%2F14=tan%28%2222%B0%22%29
SX+=+14tan%28%2222%B0%22%29

We use the larger (green) right triangle BWX to find BX

BX%2FWX=BX%2F14=opp%2Fadj=tan%28%2255%B0%22%29

BX%2F14=tan%28%2255%B0%22%29
BX+=+14tan%28%2255%B0%22%29

SB = BX - SX = 14tan(55°) - 14tan(22°) = 14[tan(55°) - tan(22°)]

= 14(1.428148007 - 0.4040262258) = 14(1.024121781)=14.33770493 meters

Edwin