Answer:
x = 16√3
y = 8√3
z = 24
Step-by-step explanation:
From the figure attached,
By applying cosine rule in ΔABD,
cos(45°) = [tex]\frac{\text{Adjacent side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2} }=\frac{z}{24\sqrt{2} }[/tex]
z = 24
By applying sine rule in ΔABD,
sin (45°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{1}{\sqrt{2} }=\frac{AD}{24\sqrt{2} }[/tex]
AD = 24
By tangent rule in ΔADC,
tan(60)° = [tex]\frac{\text{Opposite side}}{\text{Adjacent side}}[/tex]
[tex]\sqrt{3}=\frac{AD}{DC}[/tex]
[tex]\sqrt{3}=\frac{24}{y}[/tex]
y = 8√3
Similarly, by sine rule in ΔADC,
sin(60°) = [tex]\frac{\text{Opposite side}}{\text{Hypotenuse}}[/tex]
[tex]\frac{\sqrt{3} }{2}= \frac{AD}{AC}[/tex]
[tex]\frac{\sqrt{3} }{2}= \frac{24}{AC}[/tex]
AC = 16√3
x = 16√3
