Sailboat question

Question

A sailboat drops a 455 m anchor line and drifts until the line is tight. If the anchor line makes an angle of 80° with the water line, how deep is the water? (3 marks)

Answer 1

The 455m rope forms a hypotenuse of a right triangle. The depth (x) is the vertical measurement opposite the 80^ο angle between the water line and the rope. Sine is opp/hyp

sin 80^ο = 0.9848 = x/455

x = 0.9848(455) ≅ 448m depth.

The answer makes sense because if the boat hadn't drifted and the anchor was directly under it, the taut rope would mean a depth of 455m. 80^ο is pretty close to a right angle, so the depth is just a bit less than 455m.