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:
[tex]tan\ (40) =\frac{opposite}{adjacent}[/tex]
⇒ [tex]tan\ (40) =\frac{25.17}{x}[/tex]
⇒ [tex]tan\ (40)\times x =\frac{25.17}{x}\times x[/tex]
⇒ [tex]tan\ (40)\times x =25.17[/tex]
⇒ [tex]\frac{tan\ (40)\times x}{tan\ (40)} =\frac{25.17}{tan\ (40)}[/tex]
⇒ [tex]x =\frac{25.17}{0.839}[/tex]
⇒ [tex]x= 30[/tex]
Length of the rope between the boat and the dock is 'x' = 30 feet.
