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Need help with this. Find the value of each variable.

Need help with this. Find the value of each variable.-example-1

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Answer:

Explanation:

By applying sine rule in ΔACD,

cos(30°) =
\frac{\text{Adjacent side}}{\text{Hypotenuse}}

cos(30°) =
(CD)/(AD)


(√(3) )/(2)=(z)/(24)

z =
8√(3)

By applying cosine rule in ΔACD,

sin(30°) =
\frac{\text{Opposite side}}{\text{Hypotenuse}}

sin(30°) =
(AC)/(CD)


(1)/(2)=(AC)/(24)

AC = 12

By applying tangent rule in ΔACB,

tan(45°) =
\frac{\text{Opposite side}}{\text{Adjacent side}}

1 =
(AC)/(BC)

y = 12

By applying sine rule in ΔACB,

sin(45°) =
(BC)/(AB)


(1)/(√(2))=(y)/(x)

x = y(√2)

x = 12√2

Need help with this. Find the value of each variable.-example-1
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