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.
A number by itself is useful, but it is far more useful to know how accurate or certain that number is.