exchemist
Valued Senior Member
OK, I've finished my gardening and have an hour to spare before tea, so let's have a look.
By my calculation, the side of the square is approx. 1.777, if I have not made any error applying the Sine Rule and I've done my Tan⁻¹ correctly. (Like any physical scientist, I am alert to the possibility of errors in my algebra and arithmetic.)
Motor Daddy can't do it at all, of course. He just wants to bugger people up and then dance around chortling about it.
I give my working below so others can check it and correct if necessary:-
1) Angle between left hand vertical and 1st rising diagonal is Tan⁻¹ 2.5/2 = 51.34⁰. This is also the angle between the same rising diagonal and left hand edge of the square (alternate angles).
2) Angle between same diagonal and central horizontal is 90-51.34 = 38.66⁰.
3) Triangle formed by left hand edge of square and the 2 diagonals extending to the left edge of the figure is isosceles, with apex angle 2 x 38.66⁰ = 77.32⁰ and base angles 51.34⁰. So we have all the angles. If we can find the length of a side of this triangle, we can find the length of its base by the Sine Rule.
4) Considering now the triangle formed by the left hand corner of the figure, the left hand corner of the square and the first rising diagonal, the upper left angle is 45⁰ and the lower left angle was worked out in (1), so the angle at the corner of the square will be 83.66⁰. So we have all the angles. But we also know the left hand side is 2 units in length. So Sin 83.66⁰/2 = Sin 45⁰/x, where x is the unknown length of the portion of the rising diagonal between the left hand side of the figure and the corner of the square. So x = 2.Sin 45⁰/Sin 83.66⁰ = 1.423.
5) So now, returning to our triangle in (3), we can apply the Sine Rule again and say: Sin 51.34⁰/1.423 = Sin 77.32⁰/s, where s is the unknown length of the base of the triangle formed by the side of the square. So s = 1.423 . Sin 77.32⁰ / Sin 51.34⁰ = 1.777.
By my calculation, the side of the square is approx. 1.777, if I have not made any error applying the Sine Rule and I've done my Tan⁻¹ correctly. (Like any physical scientist, I am alert to the possibility of errors in my algebra and arithmetic.)
Motor Daddy can't do it at all, of course. He just wants to bugger people up and then dance around chortling about it.
I give my working below so others can check it and correct if necessary:-
1) Angle between left hand vertical and 1st rising diagonal is Tan⁻¹ 2.5/2 = 51.34⁰. This is also the angle between the same rising diagonal and left hand edge of the square (alternate angles).
2) Angle between same diagonal and central horizontal is 90-51.34 = 38.66⁰.
3) Triangle formed by left hand edge of square and the 2 diagonals extending to the left edge of the figure is isosceles, with apex angle 2 x 38.66⁰ = 77.32⁰ and base angles 51.34⁰. So we have all the angles. If we can find the length of a side of this triangle, we can find the length of its base by the Sine Rule.
4) Considering now the triangle formed by the left hand corner of the figure, the left hand corner of the square and the first rising diagonal, the upper left angle is 45⁰ and the lower left angle was worked out in (1), so the angle at the corner of the square will be 83.66⁰. So we have all the angles. But we also know the left hand side is 2 units in length. So Sin 83.66⁰/2 = Sin 45⁰/x, where x is the unknown length of the portion of the rising diagonal between the left hand side of the figure and the corner of the square. So x = 2.Sin 45⁰/Sin 83.66⁰ = 1.423.
5) So now, returning to our triangle in (3), we can apply the Sine Rule again and say: Sin 51.34⁰/1.423 = Sin 77.32⁰/s, where s is the unknown length of the base of the triangle formed by the side of the square. So s = 1.423 . Sin 77.32⁰ / Sin 51.34⁰ = 1.777.
