Question

I need help with solving the problem step by step. I know that it’s a law of cosine problem

Answer 1

Given:

Two straight roads diverge at an angle of 65 degree.

One car traveling at 50 mph and other at 30 mph.

AB is the road 1 and AC ia road 2.

A is intersection of the cars. Car travels on the AC path is at 50 mph. and car on the AB path is at 30 mph.

As both car starts traveling at 2:00 pm then at 2:30 both will travel for half an hour.

So, the half the distances will be,

`\begin{gathered} AD=25\text{ } \\ AG=15 \end{gathered}`

Using cosine formula,

`\begin{gathered} DG^2=AD^2+AG^2-2(AD)(AG)\cos 65^(\circ) \\ =25^2+15^2-2(25)(15)(0.4226) \\ =25^2+15^2-316.95 \\ =533.05 \\ DG=23.09\text{ miles} \end{gathered}`

Answer: The car will apart from each other at 23.09 miles.