9514 1404 393
Answer:
54.8 km
Step-by-step explanation:
The sketch and the applicable trig laws cannot be completed until we understand what the question is.
<u>Given</u>:
two boats travel for 3 hours at constant speeds of 22 and 29 km/h from a common point, their straight-line paths separated by an angle of 39°
<u>Find</u>:
the distance between the boats after 3 hours, to the nearest 10th km
<u>Solution</u>:
A diagram of the scenario is attached. The number next to each line is the distance it represents in km.
The distance (c) from B1 to B2 can be found using the law of cosines. We can use the formula ...
c² = a² +b² -2ab·cos(C)
where 'a' and 'b' are the distances from the dock to boat 1 and boat 2, respectively, and C is the angle between their paths as measured at the dock.
The distance of each boat from the dock is its speed in km/h multiplied by the travel time, 3 h.
c² = 66² +87² -2·66·87·cos(39°) ≈ 3000.2558
c ≈ √3000.2558 ≈ 54.77
The boats are about 54.8 km apart after 3 hours.
