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#1 2006-01-09 04:42:51

sharon
Guest

i need help

An engineer measures the angle of elevation of the top of the perpendicular lighthouse as 22.
He moves 110m nearer the building and finds the angle 49. Determine the height of the lighthouse.



Help me with this problem please.

#2 2006-01-09 05:35:23

irspow
Power Member

Offline

Re: i need help

At distance x the angle to the top of the lighthouse is 49°.

   So the H = x tanθ or x tan 49°

   At distance (x + 110) meters the angle is 22° so,

  H = (x + 110) tan 22°

  The height does not change so...

   x tan 22° + 110 tan 22° = x tan 49

  Therefore x = 110 tan 22° / (tan 49° - tan 22°)

  Since H = x tan 49° = (110 tan 22° tan 49°) / (tan 49° - tan 22°)

  H ≈ 68.5 meters

Last edited by irspow (2006-01-09 05:46:08)

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