How Do You Work This Out?

[ck1]

There's a square, and inside is an equilateral triangle with the sides the same length as the square (the base of the triangle is the bottom of the square). Need to calculate the angle from the bottom left square corner, to the top of the triangle to the top left square corner.

[elliemay1]

45degrees?

[roslyn251254]

30

[JJ109]

75 degrees
The angle between the bottom left corner to the apex of the triangle is 30 degrees. (90 degrees - 60degrees)
The triangle bottom left corner of square to apex triangle to top left corner of the square is an isosceles triangle The side length of the equilateral triangle and the square are the same.
Therefore as the apex of the isosceles triangle = 30 degrees, the two base angles = (180 - 30)/2 = 150/2 = 75 degrees

It is easier to describe with a notated diagram

[fiction-factory]

Isn't the angle that's asked for just teh 30 degrees you mention near teh start of your answer jj?

[JJ109]

Lets try again - the answer is still 75 degrees

Call the square clockwise from top left, ABCD and the apex of the triangle point E. You require angle DEA

Angle ADE = 30 degrees (90 - 60 = 30)
Triangle ADE is an isosceles triangle
Angles DAE and DEA are the base angles and equal (180 -30)/ 2 = 75 degrees

[fiction-factory]

Actually I think we need a diagram as the triangle can't be touching the top of the square. maybe we are seeing teh question differently

[sunny-dave]

JJ is correct

[fiction-factory]

Yes I agree it's 75 degrees. The question wording wasn't clear to me as to the angle needed as I'm used to your labelling conventions

[jackthehat]

http://i67.tinypic.com/eiv4fk.jpg

A graphical explanation of JJ109's answer...

[fiction-factory]

Thanks. Yes, I agree. The only query I had initially was which angle the OP wanted, but I now agree it must be this 75 degree one (the angles being 30, 75,75)

[IJKLM]

Well...

First, I suspect the triangle is not an equilateral. Probably isosceles.
An equilateral triangle will not fit inside a square of the same length.

So the triangle DEA (using JJ's convention) has two short sides of 1 and 2 units. The hypotenuse is therefore Sq. Root(5) or 2.2 something.

The angle is thus arctan 2 (or arcsin (1/root [5]), which is equal to 1.107 radians or 63.435 degrees:

[sunny-dave]

IJKLM - the top of the triangle isn't on the perimeter of the square - so it can be equilateral

[fiction-factory]

IJKLM- that's because you've assumed the triangle apex is on the top line of the square whereas it lies within the square (see jth's diagram)

[IJKLM]

OK. I see that if the OP is strictly accurate, but one can easily imagine that the OP has been a bit sloppy and seen the isosceles as an equilateral.

*shrug* the OP can work out which situation meets their needs most accurately.

[Prudie]

For once I also agree it's 75, phew

[ck1]

Thanks all for the answers (no sloppiness here, definitely an equilateral triangle!)