TG EAMCET 3 May 2025 Shift 2 Paper

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=16km
The second ship travels at 12 km per hour. In 2 hours, it travels:
12×2=24km
Step 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∘=‌

242+162−c2

2×24×16

Since cos‌120∘=−‌

1

2

,−‌

1

2

×2×24×16=242+162−c2
242=576,162=256,‌ and ‌2×24×16=768.‌ So, ‌−‌

1

2

×768=576+256−c2−384=832−c2
Add c2 on both sides and add 384 to both sides: c2=832+384=1216
Now, 1216=64×19. So, c=8√19
So, the distance between the ships after 2 hours is 8√19km.