Answer:
5.76 km/h
Step-by-step explanation:
The mnemonic SOH CAH TOA reminds you of the relationship between angles and sides of a right triangle. Here, we are given the side opposite the angle (angle of depression), and we want to find the adjacent side (distance from shore).
Tan = Opposite/Adjacent
tan(4°) = (height of tower)/(distance from shore)
tan(4°) = (50 m)/(distance from shore)
Then the distance from shore is ...
distance from shore = (50 m)/tan(4°) ≈ 715.03 m
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At the second sighting, the distance from shore is ...
distance from shore = (50 m)/tan(12°) ≈ 235.23 m
So, the distance traveled in 1/12 hour is ...
715.03 m - 235.23 m = 479.80 m
and the speed in km per hour is ...
speed = 0.4798 km/(1/12 h) = 5.7576 km/h
The speed of the boat is about 5.76 km per hour.
