I have a square, divided up into 4 quadrants and need to know which quadrant a point lies in. I know the length of all 3 sides of the triangle (the edge of the square is 90', and the other two sides are lengths from 2 adjacent corners to the point, e.g. 48' and 63'). How do I best figure the angles of the triangle in order to calculate where the point lies, or is there another way to do this?
Let's suppose the given square and point P are like this:
You are asked to determine whether P is in the upper left,
upper right, lower left, or lower right quadrants.
One way of course is to draw it accurately and see. The above
is drawn accurately. Here we can see that it is in the bottom
left quadrant. However, "looking and seeing" does not count.
So we will have to calculate it. Have you had the "law of
cosines"? It can be done with or without that law. I will
assume you have studied that law. If you haven't please post
again telling me you have not had the law of cosines and I
will show you the other way.
We can calculate angle BAP by the law of cosines:
=
=
=
Using the inverse cosine we get
= 41.85879221°
Now we draw altitude PQ.
All we need do now is calculate AQ and PQ
=
=
=
= 35.75'
=
=
=
= 32.03025913'
So we see that both AQ and PQ are less
than 45' (half of 90') this shows that the
point P is in the lower left quadrant.
If AQ were greater than 45' and PQ less than 45',
then P would have been in the lower right quadrant.
If AQ were less than 45' and PQ were greater than 45',
then P would have been in the upper left quadrant.
If both AQ and PQ were greater than 45', then P would
have been in the upper right quadrant.
Edwin