Question

Find the missing part for A, Y, Z, and B.

Answer 1

All (3) of the triangles are similar to one another, and they have the 30-60-90 interior-angle pattern. This allows us to establish the following relations.


`a+b=2x\implies x=\frac{15}2`



`z=\sqrt3\,x\implies z=\frac{15\sqrt3}2`



`\frac ax=\frac x{a+b}\implies a(a+b)=x^2\implies15a=(15^2)/(2^2)\implies a=\frac{15}4`



`a+b=15\implies b=15-\frac{15}4=\frac{45}4`



`y=\sqrt3\,a\implies y=\frac{15\sqrt3}4`