value of segment DE

Question

Using the special triangles, determine the exact value of segment DE. Segments d= BA and e = BC have length 6. Express your answer in simplified radical form.

Answer 1

know CE=3 (opposite side from 30 degrees is half hypotenuse in right triangle)

BE=√(6²-3²)=√27=3√3

know BD=6/√2=3√2 (BCD is a 45 degree right triangle)

BD²+BD²=6²

DE=BE-BD

Answer 2

BE = 3√3; BD = 3√2; so, DE = 3(√3 - √2)