Question

Find x.
A. 21(route)2
B. 7
C.21(route)3/2
D. 21(route)2/2

Answer 1

Option (D)

Explanation:

By applying Sine rule in the right ΔABD,

Sin(A) =
`\frac{\text{Opposite side}}{\text{Hypotenuse}}`

Sin(60)° =
`\frac{\text{BD}}{\text{AB}}`

`(√(3))/(2)=\frac{\text{BD}}{7√(3)}`

BD =
`7√(3)* (√(3) )/(2)`

=
`(21)/(2)`

Now by applying Cosine rule in the right ΔBDC,

Cos(45)° =
`\frac{\text{Adjacent side}}{\text{Hypotenuse}}`

`(1)/(√(2))=((21)/(2))/(x)`

x =
`(21)/(2)* √(2)`

x =
`(21√(2))/(2)`

Therefore, Option (D) is the correct option.