Question

Two boats start their journey from the same point A and travel along directions AC and AD, as shown below:

What is the distance, CD, between the boats?

230.9 ft
284.3 ft
115.5 ft
173.2 ft

Answer 1

230.9 ft

Explanation:

person above said it was correct answer

Answer 2

Option (1)

Explanation:

By applying tangent rule in ΔABD,

tan(30°) =
`\frac{\text{Opposite side}}{\text{Adjacent side}}`

=
`(AB)/(BD)`

BD =
`\frac{AD}{\text{tan}(30)}`

BD =
`(200)/((1)/(√(3) ) )`

BD = 200√3 ft

By applying tangent rule in ΔABC,

tan(60°) =
`(AB)/(BC)`

`√(3)=(200)/(BC)`

BC =
`(200)/(√(3))`

Since, CD = BD - BC

CD = 200√3 -
`(200)/(√(3))`

= 346.41 - 115.47

= 230.94 ft

≈ 230.9 ft

Therefore, Option (1) will be the correct option.