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#1 2006-01-08 05:42:51

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 2006-01-08 06:35:23

irspow
Member
Registered: 2005-11-24
Posts: 455

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 (2006-01-08 06:46:08)

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