A boat anchored to the sea floor has a rope making a 50° angle with the surface. If the rope is 150 feet long, to the nearest foot, what is the depth of the water?

To find the depth of the water, we can think of the situation as a right triangle where the rope forms the hypotenuse. The angle between the rope and the surface of the water is 50 degrees. To find the depth, we can use the sine function from trigonometry, which relates the angle of a right triangle to the lengths of the opposite side (depth of the water) and the hypotenuse (length of the rope).

The formula to find the depth in this case is:

[ \text{Depth} = \text{Hypotenuse} \times \sin(\text{Angle}) ]

By substituting the values into the formula:

[ \text{Depth} = 150 , \text{feet} \times \sin(50^\circ) ]

Calculating ( \sin(50^\circ) ) yields approximately 0.7660. Then, we multiply:

[ \text{Depth} \approx 150 \times 0.7660 ]

[ \text{Depth} \approx 114.9 , \text{feet} ]

Rounding this value to the nearest foot gives a depth of approximately 115 feet. This matches the chosen answer