Question

How far apart were they after 2 hours? In miles

Answer 1

Given:

Jan's speed = 5 mph

Jan's bearing = N12° E

Dean's speed = 3 mph

Dean's bearing = N31°W

Let's find the distance between themafter 32 hours.

First sketch a diagram representing this situation.

Where:

x is the distance both of them.

Now, after 2 hours, we have:

Distance travelled by Jan after 2 hours = 5 mph x 2 = 10 miles

Distance travelled by Dean after 2 hours = 3 mph x 2 = 6 miles

Now, let's solve for x using the cosine rule:

`\begin{gathered} x=√(10^2+6^2-2(10)(6)cos(31+12)) \\ \\ x=√(100+36-120cos(43)) \\ \\ x=√(136-87.76) \\ \\ x=√(46.24) \end{gathered}`

Solving further:

`x=6.9`

Therefore, he distance tbetween them after 2 hours is 6.9 miles.

ANSWER:

6.9 miles