Answer:
AB = 42.15 units
Step-by-step explanation:
In triangle ABD,
By applying Cosine rule in this triangle,
cos(30)°= [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{\sqrt{3} }{2}[/tex] = [tex]\frac{AD}{AB}[/tex]
[tex]\frac{\sqrt{3}}{2}=\frac{AD}{47}[/tex]
AD = [tex]\frac{47\sqrt{3}}{2}[/tex]
By applying tangent rule in ΔACD,
tan(44)° = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
tan(44)° = [tex]\frac{AD}{x}[/tex]
0.9657 = [tex]\frac{\frac{47\sqrt{3}}{2}}{x}[/tex]
0.9657 = [tex]\frac{47\sqrt{3}}{2x}[/tex]
x = [tex]\frac{47\sqrt{3}}{2(0.9657)}[/tex]
x = 42.15
≈ 42.2 units
