An observer standing on the top of a lighthouse 150 m above the sea level watches a ship sailing away. As he observes, the angle of depression of the ship changes from $50^{\circ}$ to $30^{\circ}$. Determine the distance travelled by the ship during the period of observation. Give your answer correct to the nearest meter. (Use Mathematical Table for this question.)
Explanation
To find the distance travelled by the ship, we need to find the difference between the two distances of the ship from the lighthouse. We can use trigonometry to find these distances. Let's denote the distance of the ship from the lighthouse at the first observation as x1 and at the second observation as x2. Using the tangent function, we have tan(50°) = 150/x1 and tan(30°) = 150/x2. Solving for x1 and x2, we get x1 = 150/tan(50°) and x2 = 150/tan(30°). The distance travelled by the ship is x1 - x2. Using a mathematical table, we can find the values of tan(50°) and tan(30°) and calculate the distance travelled by the ship.
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