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YouAreAwesome

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Thread moved from the technical math forums to the schoolwork forum

**TL;DR Summary:**My student had this in an exam. Have I solved it correctly?

**Question: Calculate the exact value of x.**

First note we've not been provided any numerical lengths, therefore the expression for x will include at least two variables, one to account for the variable size of ΔCDB, and one to account for the variable size of ΔEBA.

Next note that by the angle sum of a triangle∠CBD=∠BAE meaning the triangles CDB and EBA are equiangular, and therefore similar.

My attempt is to write x in terms of the length a, and the scale factor from ΔEBA to ΔCDB of k.

In ΔCDB:

Tan(Pi/3) = (a+x)/g

g = (a+x)/√3

Now scaling ΔEBA by k to equal ΔCDB:

ka = g

ka = (a+x)/√3

ka√3 = a+x

x = ka√3-a

x = a(k√3-1)

Can someone please confirm this expression to see if I have missed a trick to simplify this even further or made a mistake somewhere? The question seems too difficult for the level my student is at and I wonder if the question is missing information.

Appreciate any input.

Cheers