Question

If two trucks leave a given city on highways making an angle of 132 degrees with one another, traveling at 45 and 55 miles per hour, respectively, what is the distance between the trucks 2 hours later

Answer 1

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.

Answer 2

Answer:

183 miles to the nearest mile.

Step-by-step explanation:

Distance =Speed X Time

Distance of Truck B from point A=45 X2 =90 miles

Distance of Truck C from point A=55 X2 =110 miles

Angles between them, BAC=132°

We want to find the Distance BC denoted by a between the trucks.

Using Cosine Rule,

a²=b²+c²-2bcCos A

=90²+110²-(2X90X110XCos132°)

=33448.79

a=√33448.79

BC=182.89 miles

The distance between the trucks is 183 miles to the nearest mile.