Arope 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?

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° =

Hence the length of the rope needed is 39.16 ft