LAST PROBLEM- i dont get it at all!
your image doesnt enlarge. i zoomed in and i think i see
80 4 x 7 35 5 7 y w z 5 v o 4
is this correct?
if it is then we begin with triangle 80 4 x 7
a straight line is 180* with itself so the angle next to 80 is 180-80=100
angles in a triangle add up to 180 so
x+100+35=180.
x+135=180
x=180-135=45
now the other triangle.
the other triangle has 3 sides the same as this triangle so its the same triangle.
o=x=45
v=100
w=35
because of the two parallel lines
o=y=45
again straight lines give 180* so
you can finish up
Hi Idontgetit,
Do you remember when you drew a triangle with a compass and ruler?
If you were given the 3 side lengths, you'd have drawn one side,
then used your compass to draw circles at the ends of that line, whose
radii were the lengths of the other 2 sides.
You could then see that the triangle was unique, as you were left with
a pair of identical triangles, whose corresponding angles and corresponding side lengths were all the same.
If you are unfamiliar, then you should draw this for any triangle you like.
In your diagram, as pointed out by Krahl, the 2 triangles have all 3 sides of the exact same lengths, therefore these triangles are identical.
Or you could say, we have the same triangle in 2 different positions.
Be sure about this first.
Now, if you imagine the triangle on the left is hinged to the double-ended arrow and you can turn it about that hinge, then you may rotate this triangle until it is in the exact same orientation as the second triangle.
Doing this causes "x" to correspond with "u",
35 degrees to correspond to "w",
the unmarked angle to correspond with "v", which is 180-80=100 degrees.
The angle "y" equals the angle "u" also if you understand the angles when
you cross 2 parallel lines with a single line.
Finally, z is 180-(w+y) degrees.
$\displaystyle u=x$
$\displaystyle w=35$
$\displaystyle v=80$
$\displaystyle x=(80+35)-180$
$\displaystyle y=\frac{7sin(x-90)}{7}$
$\displaystyle z=(y+w)-180$
note: that the left most triangle is just the right triangle at a different orientation.