Question

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

Answer 1

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