The captain drops the 3- foot- long anchor and lets out 100 feet of anchor rope. The boat floats away from where the anchor was dropped until the anchor rope becomes straight due to the tide. The captain uses the yardstick and determines that a total 27 inches of the anchor rope is above the water. Using the inclinometer, the captain determines that the angle of depression of the anchor rope is 42 degrees. The captain knows the water is parallel to the bay floor.
How do I determine the distance, to the nearest inch, from point p, the place where the anchor rope leaves the boat, to the water line?
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The first and last sentences of this paragraph are only meant to confuse/distract you. This questions boils down to simple trigonometry:
We have a right triangle with hypotenuse = 27 inches, and an angle of 42 degrees. We want to know the length of the side of the triangle opposite to the 42 degrees, so we use the sine function. (Remember, sine = opposite/hypotenuse)
sin(42) = opposite/(27 inches)
27*sin(42) = opposite
opposite = 18.07 inches
round to the nearest inch: opposite = 18 inches