Please refer the attached figure for better understanding of the solution
Here we are given that the angle of depression is 40°
And the height of the boat from the water is 25.17 ft
we need to find the length of the rope used which we can take as x
We can see that sin is the ratio that corresponds to the opposite side and the hypotenuse sides of the triangle formed
so we have
sin 40° = [tex]\frac{25.17}{x}[/tex]
[tex]x=\frac{25.17}{sin 40}[/tex]
[tex]x=\frac{25.17}{0.6427}[/tex]
[tex]x= 39.16[/tex]
Hence the length of the rope needed is 39.16 ft
