Question

What is the value of x? Please show step by step.

Answer 1

Start by using trig to find the length of the line LJ

The triangle KJL (big right angled triangle) has been given the following dimensions

Hypotenuse = $8 \sqrt{2}$
The adjacent angle is 30 degrees

Since we have the hypotenuse and the  angle we must use the equation 
opposite = Sin(angle) x Hypotenuse

Opposite= sin30 x $8 \sqrt{2}$

Opposite= $4 \sqrt{2}$

Therefore line LJ is $4 \sqrt{2}$


Now look at the smaller right angled triangle (LMJ) 

Hypotenuse is the line LJ which is $4 \sqrt{2}$

The adjacent angle is 45

Since we have hypotenuse and angle we must use the equation opposite = sin(angle) * h

therefore 
x= $4 \sqrt{2}$ * sin45= 4