Trignometry

[Benji]

Please help me with this practical problem.
1) ABC is a triangle
2) AB is vertical and A is uppermost,
3) AC=61 units,
4) BC=60 units,
5) AB is variable, point B can only move vertically up or down,
6) D is a point on the extension of BC, D is on the side of C and CD=61 units.

Questions:
1) As B moves up from its lowest point (ABmax = 61 +60 = 121 units), will point D ever rise above the horizontal line through A?
2) If it does, by how much vertical distance.

 

[Dr.Peterson]

Please help me with this practical problem.
1) ABC is a triangle
2) AB is vertical and A is uppermost,
3) AC=61 units,
4) BC=60 units,
5) AB is variable, point B can only move vertically up or down,
6) D is a point on the extension of BC, D is on the side of C and CD=61 units.

Questions:
1) As B moves up from its lowest point (ABmax = 61 +60 = 121 units), will point D ever rise above the horizontal line through A?
2) If it does, by how much vertical distance.

The simple answer is No. D will never lie above the level of A.

First, here is a picture, made with GeoGebra:


The red curve is the locus of D, and you can see that it doesn't rise above A. (Make sure I've interpreted the question correctly!)

Second, here is a reason: ACD is an isosceles triangle; I have drawn in the angle bisector of the apex angle at C, which is perpendicular to the base, AD. But the other broken line, the bisector of angle ACB, is perpendicular to the first angle bisector, and therefore parallel to AD. Because AC > BC, this will always slant down to the right.

Does that help?

 

[Benji]

Than you.

Thank you Dr. Peterson for your help.
I still have a problem with it.
The question was to do with the opening profile of an "up and over" garage door, ignoring the bottom half of door. I'm trying to see if i can use the old garage door in my new extension. The problem really is, the effective thickness (measured from the pivot point on door) is 70mm. So when you open the door, the top edge of door rises up and hit the ceiling joist. Unfortunately, the joists are the same level as the top of the door. I think it goes up by about 35 mm. I worked this out on my AutoCAD lite.
I think I'll have to have the height of door reduced or buy a new one.
Many thanks for your help.
Benji

 

[Dr.Peterson]

Thank you Dr. Peterson for your help.
I still have a problem with it.
The question was to do with the opening profile of an "up and over" garage door, ignoring the bottom half of door. I'm trying to see if i can use the old garage door in my new extension. The problem really is, the effective thickness (measured from the pivot point on door) is 70mm. So when you open the door, the top edge of door rises up and hit the ceiling joist. Unfortunately, the joists are the same level as the top of the door. I think it goes up by about 35 mm. I worked this out on my AutoCAD lite.
I think I'll have to have the height of door reduced or buy a new one.
Many thanks for your help.
Benji

Yes, when I add some thickness to my model, I see as expected that while the middle of the top of the door (point D) moves horizontally away from A, the corner of the door will initially rise at some steady angle.

Thicknesses mess up ideal models, don't they?