# Cabin trigonometry

#### jpend

##### New member
Hi all! I'm a non-student adult who would love some input on some triangles I noticed at our cabin. Please let me know if this post is inappropriate for the site. I'll seek help elsewhere.

The window in the photo below is composed of right-angle triangles. But the triangle on the perpendicular wall, a result of light pouring through the right pane of the window, is an isoceles triangle. How is this possible? Many thanks!

View attachment 29187

#### lev888

##### Elite Member
Hi all! I'm a non-student adult who would love some input on some triangles I noticed at our cabin. Please let me know if this post is inappropriate for the site. I'll seek help elsewhere.

The window in the photo below is composed of right-angle triangles. But the triangle on the perpendicular wall, a result of light pouring through the right pane of the window, is an isoceles triangle. How is this possible? Many thanks!

View attachment 29187
First of all, a right-angle triangle can be isosceles.
Cut out a paper triangle and experiment. See how its shadow changes depending on the angle between light rays and the planes of the triangle and the surface where the shadow is.

#### Subhotosh Khan

##### Super Moderator
Staff member
Hi all! I'm a non-student adult who would love some input on some triangles I noticed at our cabin. Please let me know if this post is inappropriate for the site. I'll seek help elsewhere.

The window in the photo below is composed of right-angle triangles. But the triangle on the perpendicular wall, a result of light pouring through the right pane of the window, is an isoceles triangle. How is this possible? Many thanks!

View attachment 29187
Did you delete or move your attachment ?

#### jpend

##### New member
Great idea about cutting out a paper triangle to experiment! I'll try that, thanks!
I'm not sure what happened with the attachment. Here it is again. Fingers crossed it stays put!

#### lev888

##### Elite Member
Great idea about cutting out a paper triangle to experiment! I'll try that, thanks!
I'm not sure what happened with the attachment. Here it is again. Fingers crossed it stays put!

View attachment 29268
Make a V sign with your fingers at your eye level. Note the angle between the fingers. It's not 90 but it doesn't matter. Start turning your hand around the vertical axis until one finger disappears behind the other. Note how the angle changes from the initial value to 0.

#### Dr.Peterson

##### Elite Member
Great idea about cutting out a paper triangle to experiment! I'll try that, thanks!
I'm not sure what happened with the attachment. Here it is again. Fingers crossed it stays put!

View attachment 29268
I just took two pictures of a 30-60-90 triangle from different angles:

The point, mathematically, is that projection doesn't preserve angles. Shadows and photos are essentially the same idea.

This is an everyday phenomenon; but your picture is particularly dramatic. It also shows (in the shadow on the railing) that projection onto a parallel plane does preserve angles.

#### jpend

##### New member
Thank you @lev888 and @Dr.Peterson for your explanations! You're right, this is an everyday phenomenon, that I understand intuitively. But the particular example I shared made me pause...
This forum is great, thanks for your help!

#### mmm4444bot

##### Super Moderator
Staff member
not sure what happened with the [original] attachment
Could've been a system glitch, but attachments will fail when quoted or pasted. You may use the preview button before submitting posts, to see issues.