Answer: The distance between the trucks after 2 hours is 183 miles
Step-by-step explanation:
As the truck head towards their respective destinations, we are required to find the distance between them after they have travelled for 2 hours.
Now, it is important that we firstly determine the distance, the respective trucks must have travelled after 2 hours:-
Since Truck A travelled at a speed of 45 miles per hour, the distance it covers after 2 hours will be:
45 miles ------- 1 hour
? miles ------2hours
= 2/1 × 45 = 90 miles
For truck B, it travelled at a speed of 55 miles per hour, the distance it covers after two hours:-
= 55 × 2 = 110 miles.
You can see the attached to understand that we are basically required to find a side of a triangle after being given 2 sides of the triangle (90 miles and 110 miles)
To determine the third side of the triangle and having a prior knowledge that the 2 trucks were at an angle of 135° when they're set-off; we then make use of cosine rule to find the distance between the trucks after 2 hours.
c^2 = a^2 + b^2 - (2×a×b cos C)
Here, a = distance covered by truck A = 90 miles
b= distance covered by truck B = 110miles
c= distance between the trucks
C= the angle between the trucks= 132°
c^2= 90^2 + 110^2 - (2×90×110 cos 132°)
c^2 = 8100 + 1200 - (19800 cos 132°)
c^2 = 8100 + 12100 + 13248.786
c^2 = 33448.786
c = √33448.786
c = 182.89
Therefore the distance between the two trucks after 2 hours is approximately 183 miles.
