Area of isosceles triangle

[y0ssar1an22]

I'm trying to figure out the area of an isosceles triangle when all you know is that the 2 sides are 1 unit in length.

The only other info you have is that making a rectangle results in a few 90° angles.

Can also not use sin, tan, etc.

See my hand written scribbles attached - sorry, not very good at using programs to make this look somewhat neater!

The target area is outlined in red, called B. 2 other triangles, equal in area called A made via a rectangle. The dotted line is something that may prove useful.

And 1 error to note, Area B should be area of rectangle less area of (2)(A). My notes have that incorrect.

Many TIA

And if that can then be done, can it be done without using the 90°?

 

[tkhunny]

Does your description constitute a unique triangle?

 

[Dr.Peterson]

I'm trying to figure out the area of an isosceles triangle when all you know is that the 2 sides are 1 unit in length.

The only other info you have is that making a rectangle results in a few 90° angles.

Can also not use sin, tan, etc.

See my hand written scribbles attached - sorry, not very good at using programs to make this look somewhat neater!

The target area is outlined in red, called B. 2 other triangles, equal in area called A made via a rectangle. The dotted line is something that may prove useful.

And 1 error to note, Area B should be area of rectangle less area of (2)(A). My notes have that incorrect.

The two side lengths are not enough to determine the figure. Here are two isosceles triangles with legs 1 unit long, with obviously different areas:


The fact that a rectangle consists of right angles is not a fact about this triangle.

Where did this assignment come from?

Many TIA

Transient Ischemic Attacks? No, thanks.

 

[y0ssar1an22]

Does your description constitute a unique triangle?

No, you are given the 2 sides. they can be any unit you wish (but equal).

 

[y0ssar1an22]

The two side lengths are not enough to determine the figure. Here are two isosceles triangles with legs 1 unit long, with obviously different areas:
View attachment 22362

The fact that a rectangle consists of right angles is not a fact about this triangle.

Where did this assignment come from?


Transient Ischemic Attacks? No, thanks.

not an assignment.

I'm trying to figure out if you can determine the area of an isosceles triangle without the use of cos/tan and the rest of those functions.

 

[y0ssar1an22]

My conjecture is that curves do not exist.

therefore any circle can be broken down into a series of isosceles triangles.

with 360 triangles, you have the 1st degree of accuracy. with 720 slices of the cake you have the 2nd degree of accuracy. all the way down to the planck length.