x = 73.21
Step-by-step explanation:
Consider triangle ABC. Since angle A is 45° and side BC is 100, then side AB is also 100.
Now consider triangle ABD. With angle A equal to 60°, we can use the definition of tangent to find the value of x:
tan 60 = BD/AB
sqrt(3) = (x + 100)/100
or
x + 100 = 100sqrt(3)
x = 100[sqrt(3) - 1]
= 73.21
