Question

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Answer 1

The length of the rope between the boat and the dock is of 30 feet.

Explanation:

Given:

tan(40) ≈ 0.839

Angle of depression = 40 (deg)

Distance between boat and the floor of the ocean = 25.17 feet

If we look into the diagram we can see that,they form 2 right angled triangle.

Where we can say that :

Distance between boat and dock = Rope's distance = Base of the triangle.

Let the length of the rope be 'x' feet.

Considering the dotted triangle:

`tan\ (40) =(opposite)/(adjacent)`

⇒
`tan\ (40) =(25.17)/(x)`

⇒
`tan\ (40)* x =(25.17)/(x)* x`

⇒
`tan\ (40)* x =25.17`

⇒
`(tan\ (40)* x)/(tan\ (40)) =(25.17)/(tan\ (40))`

⇒
`x =(25.17)/(0.839)`

⇒
`x= 30`

Length of the rope between the boat and the dock is 'x' = 30 feet.