Question

Can someone help me on this question?

Answer 1

x = 19.6

Explanation:

By applying cosine rule in ΔBCD,

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

=
`(BC)/(BD)`

`(√(3))/(2)=(BC)/(16)`

BC =
`8√(3)`

Now, by applying sine rule in ΔBAC,

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

`(1)/(√(2))=(AB)/(BC)`

`(1)/(√(2))=(x)/(8√(3))`

x =
`8√(6)`

x = 19.59

x ≈ 19.6