Find the value of x and y:
Sorry, but that's all it said: I can post the first part though (already solved it): A frame in the shape of the simple scissors truss shown a the right below can be used to support a peaked roof. The weight of the roof compresses some parts of the frame, while other parts are in tension. A frame made with s segments joined at j points is stable is s is greater to or less than 2j-3. In this truss, 9 segments connect 6 points. Verify that the truss is stable. Then find the values of x and y.
For convenience I'm going to label the points top down and left to right with A, B, C, etc.
There are two right triangles: triangle BDE and CDG. The right angles are angles DBE and DCG, though the diagram doesn't make it look like that.
The problem I am having here is that the apex angle EAG is not specified. We may have a number of possible apex angles for this construction, all of which give different x and y values.
-Dan
Hello, icebreaker!
Find the value of $\displaystyle x$ and $\displaystyle y$.Code:A * /*\ / * \ y / * \ y / * \ / * \ / * \ F * 5 * 5 * E / * * * \ 12 / O \ 12 / 13 * * * 13 \ / * * * \ B * - - - - - * - - - - - * C x D x
Triangles OFB and OEC have sides: 5, 12, 13.
. . Since $\displaystyle 5^2 + 12^2 \,=\,13^2$, they are right triangles.
Then: $\displaystyle \angle OFB = \angle OEC = 90^o$
In right triangle $\displaystyle BEC\!:\;\;BC^2 \:=\:BE^2 + EC^2$
. . That is: .$\displaystyle (2x)^2\:=\:18^2+12^2\quad\Rightarrow\quad4x^2\,=\, 468\quad\Rightarrow\quad x^2\,=\,117$
Therefore: .$\displaystyle x \:=\:\sqrt{117}\quad\Rightarrow\quad\boxed{x \,=\,3\sqrt{13}}$
In right triangle $\displaystyle BEA\!:\;\;FA^2 \:=\:BE^2 + AE^2$
. . That is: .$\displaystyle (y+12)^2\:=\:18^2 + y^2\quad\Rightarrow\quad y^2 + 24y + 144\:=\:324 + y^2$
Therefore: .$\displaystyle 24y \,=\,180\quad\Rightarrow\quad\boxed{y \,=\,\frac{15}{2}}$