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#1 2011-11-17 03:23:15

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 95,982

The lighthouse

Two landmarks are on the opposite sides of a tower. They measure the angles of elevation from the landmarks to the top of the tower as 30° and 45°. If the height of the tower is 200 meters, find the distance between the landmarks

Let's use geogebra to solve this:

1) Scale the x axis from 0 to 500 and the y axis from 0 to 200.

2) Place a point called A at (250,0). Place another point called B at (250,200).

3)Draw a line segment from A to B.

That represents the lighthouse.

4) Use the angle with a given size by clicking A then B. An angle will be drawn with vertex at B of 45° .

4) Use the angle with a given size by clicking A then B. Input 60° and check clockwise. An angle will be drawn with vertex at B of 60° .

5)Draw a line through B and A' and B and A'1.

6)Get the intersection of the line BA' and the x axis. The point will be called C.

7)Get the intersection of the line BA'1 and the x axis. The point will be called D.

8)Set rounding to 15 significant figures.

9) Measure the distance from C to D with the distance tool.

You should get 546.4101615137754. Take that over to

http://isc.carma.newcastle.edu.au/

and do an advanced lookup. Plug in 546.4101615137754 you should get.

The calculator adjusts some input to <1 and >0. We just times the answer by 1000 to turn .5464101615137754 to 546.4101615137754.

So the distance between the two landmarks is:

That is an exact answer folks, without any trigonometry!

View Image: Screenshot - 11_17_2011 , 7_53_50 AM.gif

In mathematics, you don't understand things. You just get used to them.

If it ain't broke, fix it until it is.

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