SOLUTION: Two people fishing from rowboats on a lake are 100m apart and have hooked their lines into the same sunken log. The first has 85m of line out, and the second has 68m of line out. A

Question 775652: Two people fishing from rowboats on a lake are 100m apart and have hooked their lines into the same sunken log. The first has 85m of line out, and the second has 68m of line out. Assuming that the lines both lie in the same vertical plane, meet at a point (on the log) and are taunt, how deep is the sunken log?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Two people fishing from rowboats on a lake are 100m apart and have hooked their lines into the same sunken log.
The first has 85m of line out, and the second has 68m of line out.
Assuming that the lines both lie in the same vertical plane, meet at a point (on the log) and are taut, how deep is the sunken log?
:
Draw this out, Angle A at the log, a = 100; Angle B opposite 85; Angle C opposite 68
:
We can use the law of cosines c^2 = a^2 + b^2 - 2(ab)Cos(C)
rearrange to find angle C
Cos(C) =
:
Cos(C) =
:
Cos(C) =
:
Cos(C) = .741
:
C = 42.16 degrees
:
Using the right triangle formed with the depth (d) of the sunken log
Sin(42) =
d = .67 * 85
d = 57 m is the depth of the log
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