A straight tunnel is to be dug through a hill. Two people stand on opposite sides of the hill where the tunnel entrances are to be located. Both can see a stake 530m away from the first person and 255m away from the second person. The angle determined by the two (the vertex) and the stake is 77 degrees. How long must the tunnel be?
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c²=a²+b²-2abcos(C)
c=[a²+b²-2abcos(C)]^0.5 a=255 b=530 C=77°
c=533.97m
c=[a²+b²-2abcos(C)]^0.5 a=255 b=530 C=77°
c=533.97m
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you know two sides and the included angle...use the law of cosines
c = length of the tunnel
c^2 = 530^2 + 255^2 - 2(530)(255) cos (77)
get out your calculator...make a contribution.
qed
c = length of the tunnel
c^2 = 530^2 + 255^2 - 2(530)(255) cos (77)
get out your calculator...make a contribution.
qed