Answer:
x = 42.2 units
Step-by-step explanation:
By applying tangent rule in the right triangle ΔADC,
tan(44)° = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
0.9657 = [tex]\frac{\text{AD}}{\text{DC}}[/tex]
0.9657 = [tex]\frac{AD}{x}[/tex]
AD = 0.9657x
Now we apply cosine rule in ΔADB,
cos(30)° = [tex]\frac{\text{Adjacent side}}{\text{Hyptenuse}}[/tex]
cos(30)° = [tex]\frac{\text{AD}}{\text{AB}}[/tex]
0.866 = [tex]\frac{0.9657x}{47}[/tex]
x = [tex]\frac{47\times 0.866}{0.9657}[/tex]
x = 42.15
x ≈ 42.2 units
Therefore, x = 42.2 units will be the answer.
