Answer:
Step-by-step explanation:
By applying sine rule in ΔACD,
cos(30°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
cos(30°) = [tex]\frac{CD}{AD}[/tex]
[tex]\frac{\sqrt{3} }{2}=\frac{z}{24}[/tex]
z = [tex]8\sqrt{3}[/tex]
By applying cosine rule in ΔACD,
sin(30°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
sin(30°) = [tex]\frac{AC}{CD}[/tex]
[tex]\frac{1}{2}=\frac{AC}{24}[/tex]
AC = 12
By applying tangent rule in ΔACB,
tan(45°) = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
1 = [tex]\frac{AC}{BC}[/tex]
y = 12
By applying sine rule in ΔACB,
sin(45°) = [tex]\frac{BC}{AB}[/tex]
[tex]\frac{1}{\sqrt{2}}=\frac{y}{x}[/tex]
x = y(√2)
x = 12√2
