Answer:x ≈ 6.2Step-by-step explanation:To find x using trig. ratios we require to find the hypotenuse of the right triangle on the left.From the right triangle on the right we can calculate the hypotenuse.sin53° = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{opp}{30}[/tex]Multiply both sides by 30opp = 30 × sin53° ≈ 24Thus the length of the hypotenuse of the triangle on the left is 24, hencecos75° = [tex]\frac{adjacent}{hypotenuse}[/tex] = [tex]\frac{x}{24}[/tex]Multiply both sides by 24x = 24 × cos75° ≈ 6.2