Question 1186309: Hello,
Could you please help me with this question?
Found 3 solutions by josgarithmetic, greenestamps, robertb:
Answer by josgarithmetic(39615)   (Show Source):
You can put this solution on YOUR website! Here is to get started.
Angle XZW is 90 degrees.
cos(X) is  .
cos(Y) is  .
Sum of the measures of the triangle XWZ is 180 degrees.
Answer by greenestamps(13198)  (Show Source):
You can put this solution on YOUR website!
There is no need to get involved with cosines of angles, as the other tutor did.
The whole problem can be solved with a little logical analysis and the basic concept that, in a triangle, the longest side is opposite the largest angle.
(1) Angle XZW is 90 degrees; it is clearly larger than any of the other angles.
(2) In triangle WXY, WY > XY > WX, so (angle X) > (angle W = angle XWY) > (angle Y)
And clearly angle XWZ is smaller than any of the others.
ANSWER, largest to smallest:
XZW
X
XWY
Y
XZW
Answer by robertb(5830)  (Show Source):
You can put this solution on YOUR website! Although I would agree with the arguments of @greenestamps, any student of Euclidean geometry would serve him/her well
if no assumptions were made based on the diagrams or pictures of the object. @greenestamps' (and also @ josgarithmetic's) arguments
hinges on the fact that X, Z, and Y are collinear, which would make angle XZW a RIGHT triangle.
But this is not completely clear from the drawing, as
1) Nothing in the hypothesis tells us that the figure WXY is a triangle, and so should not be initially treated as such, and consequently
2) It cannot be assumed that angle XZW is a right angle, because it wasn't stated as a hypothesis -- indeed there was no indication of a "square corner" at angle XZW.
The remedy is to first show that triangle XZW is a right triangle.
The easiest way to prove this is to use the fact that the Pythagorean theorem is an "if and only" statement,
i.e., a triangle is a right triangle if and only if the square of one side is the sum of the squares of the other two sides.
From the given figure side WZ will have length  . (We know that triangle WZY is a right triangle.)
This then will confirm that the sides of triangle XZW satisfy the Pythagorean relation:  ,
and therefore triangle XZW is indeed a right triangle. And consequently, X, Z, and Y are collinear.
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