What is the value of x? The figure shows 2 right triangles, triangle K L J with right angle J and triangle L J M with right angle M. The measure of angle L K J is 30 degrees. The measure of angle L J M is 45 degrees. The length of side K L is 8 square root 2. The length of side L M is x. Enter your answer in the box. x =

See the attached figure which represents the explanation of the problem

∵ Δ KJL is a right triangle at ∠J
∴ KL is the hypotenuse = 8√2
∵ ∠ JKL = 30°
∴ The side which faces the angle 30° will be the half of the hypotenuse because sin 30° = JL/KL = 0.5
∴ JL = 0.5 KL = 0.5 * 8√2 = 4√2

Δ JML is a right triangle at ∠M
∴ JL is the hypotenuse = 4√2  ⇒⇒⇒ (proved)
∵ ∠LJM = 45°  ,  ML = x
∴ sin 45° = x/JL
∴ x = JL sin 45° = 4√2 * (1/√2) = 4

The correct answer 
The length of side L M is x = 4