Answer:
D = 23.7 miles
Step-by-step explanation:
Given data:
[tex]\theta=84 degrees[/tex]
Time[tex] = 20 min = \frac{1}{3} hr[/tex]
Distance of A [tex]= (60 mi/hr)\times \frac{1}{3} hr =20 mi[/tex]
Distance of B =[tex] (45 mi/hr)\frac{1}{3} hr = 15 mi[/tex]
Draw a triangle.
By using cosine formula we can determine the distance between them
[tex]D^2 = 20^2 + 15^2 - 2\times 20\times 15\times cos(84)[/tex]
[tex]D^2 = 625 - 600 cos(84) [/tex]
[tex]D^2 = 625 - 63.2 [/tex]
[tex]D^2 = 561.8[/tex]
Thus D = 23.7 miles
