Refer to attached annotated figure below.
Step 1: prove triangle ABD is similar to triangle BCD
1. ∠ ADB = ∠ BDC (given)
2. ∠ BAD = 90-y; ∠ DBC= 90-y, => ∠ BAD is congruent to ∠ CBD.
=> triangle ABD is similar to triangle BCD [AA]
Step 2: find length of AD
Using Pythagoras theorem, AD^2=AB^2-BD^2 = 5^2-4^2=9
=> AD=3
Step 3: use the property that corresponding sides of similar triangles are proportional: BC/BD = AB/AD
substitute values
AB=5, AD=3, BD=4, BC=x
x/4=5/3
solve for x
x=5*4/3=20/3
or x=6.67 (to 2 decimal places)
