The tallest lighthouse in the world is the Jeddah Light. It is 133 m tall. A dhow is sailing away from this lighthouse. From the top of the lighthouse, the angle of depression to the dhow is 65° Later, the angle of depression has changed to 40°.
How far did the dhow travel during that time?
To solve this problem, we can use trigonometry and the fact that the angles in a triangle add up to 180°.
Let's call the distance between the lighthouse and the dhow "d".
We know that the angle of depression from the top of the lighthouse to the dhow is 65°, and the angle of depression later changed to 40°.
Let's call the angle between the horizontal and the line of sight from the lighthouse to the dhow, "x"
Since the angles in a triangle add up to 180°, we can say that:
x + 65 + 40 = 180
x = 75
Now, we can use the tangent function to find the distance d. We know that:
tan(x) = d / h
tan(75) = d / 133
d = 133 * tan(75)
Therefore, the dhow traveled 133 * tan(75) distance during that time.