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**sharon****Guest**

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.

**irspow****Member**- Registered: 2005-11-24
- Posts: 457

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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