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
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!
In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
No great discovery was ever made without a bold guess.