Question

A rope is used to anchor a boat to the shore. The angle of depression from the boat to the water is 40° . The height of the boat above the water is 25.17 feet. What is the length of the rope that is anchoring the boat to the shore?

Answer 1

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° = $\frac{25.17}{x}$

$x=\frac{25.17}{sin 40}$

$x=\frac{25.17}{0.6427}$

$x= 39.16$

Hence the length of the rope needed is 39.16 ft