Question

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Answer 1

Answer:

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

Step-by-step 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:

$tan\ (40) =\frac{opposite}{adjacent}$

⇒ $tan\ (40) =\frac{25.17}{x}$

⇒ $tan\ (40)\times x =\frac{25.17}{x}\times x$

⇒ $tan\ (40)\times x =25.17$

⇒ $\frac{tan\ (40)\times x}{tan\ (40)} =\frac{25.17}{tan\ (40)}$

⇒ $x =\frac{25.17}{0.839}$

⇒ $x= 30$

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