Question

What is the value of x?

Answer 1

On the left we have a 30-60-90 triangle.  Find the length of side JL:

Since sin 30 deg = |JL| / ( 8sqrt(2) ),  |JL| = 8 sqrt(2)*(1/2) = 4 sqrt(2).

Now, on the right, we have a 45-45-90 triangle with hypotenuse 4 sqrt(2).

Since c^2 = a^2 + b^2 (Pyth. Theorem), 16(2) = x^2 + x^2, or 32 = 2x^2, or 16 = x^2.  Thus, x = 4 (answer)