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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)