In exercises 11-15, find the value of x:

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)