Question

Please please help!!! i'll give you brainliest!!

Answer 1

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°) = $\frac{\text{Adjacent side}}{\text{Hypotenuse}}$

$\frac{1}{\sqrt{2} }=\frac{z}{24\sqrt{2} }$

z = 24

By applying sine rule in ΔABD,

sin (45°) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

$\frac{1}{\sqrt{2} }=\frac{AD}{24\sqrt{2} }$

AD = 24

By tangent rule in ΔADC,

tan(60)° = $\frac{\text{Opposite side}}{\text{Adjacent side}}$

$\sqrt{3}=\frac{AD}{DC}$

$\sqrt{3}=\frac{24}{y}$

y = 8√3

Similarly, by sine rule in ΔADC,

sin(60°) = $\frac{\text{Opposite side}}{\text{Hypotenuse}}$

$\frac{\sqrt{3} }{2}= \frac{AD}{AC}$

$\frac{\sqrt{3} }{2}= \frac{24}{AC}$

AC = 16√3

x = 16√3