Please help me solve this word problem

Two straight roads diverge at an angle of 65 degrees. Two cars leave the intersection at 2:00pm, one traveling at 50 mi/h and the other at 30 mi/h. How far apart are the cars at 2:30pm.
the answer is 23.1 miles

65 degrees. at 2:30 means that it is 1/2 hour.

Car A travels 25 miles and car B travels 15 miles after 30min.

Using cosine law,

a^2 = b^2 + c^2 - 2bc COS A where a = distance between them and A = 65 deg. b = 25 and c= 15

a^2 = 25^2 + 15^2 - 2(25)(15)cos 65

a^2 = 533.036

a = sqrt (533.036)
a = 23.0875

a~ 23.1

Sketch the two roads which form an angle of 65°. Each has traveled for ½ hours at 2:30 PM.

So, car 1 is 25 miles from the intersection and car 2 is 15 mi from the intersection.

The two cars and the intersection form a triangle.
Let c represent the distance from one car to the other. It is a leg of the triangle that is opposite the 65°. Use the Law of Cosines to calculate c.

To wit: c² = 25² + 15² ‒ 2(25)(15)Cos(65°) = 850 ‒ 316.9637 = 533.0363

c = √533.0363 = 23.0876

The cars are a little be more than 23.1 miles apart at 2:30 PM.

ProfRay

For this problem, you are given three pieces of information: two sides and an angle.

I set up the drawing, and I solved the problem using the law of Cosines.

Edit: I read my calculator wrong; it's 23.087, not 28.087 o.O

50(1/2) = 25 miles
30(1/2) = 15 miles
Using law of cosines,
d = sqrt[25^2 + 15^2 - 2*25*15cos(65)] = 23.1 miles