Step 1: Find how far each ship goes in 2 hours.
The first ship travels at 8 km per hour. In 2 hours, it travels:
8×2=16kmThe second ship travels at 12 km per hour. In 2 hours, it travels:
12×2=24kmStep 2: Find the angle between the directions of the ships.
The paths of the two ships make a
120∘ angle with each other. We use this angle to find the distance between them after 2 hours.
Step 3: Use the Cosine Law to find the distance between ships.
The Cosine Law formula is:
c2=a2+b2−2ab‌cos‌C where
a and
b are the distances traveled, and
C is the angle between the paths.
Let
a=24km,b=16km, and
C=120∘.
Plug these values into the formula:
cos‌120∘=‌Since
cos‌120∘=−‌,−‌×2×24×16=242+162−c2242=576,162=256,‌ and ‌2×24×16=768.‌ So, ‌−‌×768=576+256−c2−384=832−c2Add
c2 on both sides and add 384 to both sides:
c2=832+384=1216Now,
1216=64×19. So,
c=8√19So, the distance between the ships after 2 hours is
8√19km.
