Question

Two ships leave a port at the same time. Ship A travels at 20 mph in a direction N32º E, and ship B travels at 28 mph in a direction S42° E. Find the distance between the two ships after 2 hours andround off answers to the nearest miles.

Answer 1

The distance of the Ship A after 2hours;

`\begin{gathered} d=\text{speed }* time \\ d=20*2 \\ d=40m \end{gathered}`

The distance of the Ship B after 2 hours;

`\begin{gathered} d=28*2 \\ d=56m \end{gathered}`

Then, we have;

Then, using cosine rule, we have;

`\begin{gathered} p^2=a^2+b^2-2ab\cos P \\ \text{Where a=56, b=40, P=100}^o \\ p^2=(56)^2+(40)^2-2(56)(40)\cos (100) \\ p^2=4736-(-777.94) \\ p^2=5513.94 \\ p=74.25 \\ p\approx74miles \end{gathered}`

The distance between the two ships after 2 hours is 74miles.