This is the question:
Two aircraft, A and B, leave an airport at the same time. A flies on a course of 81 degrees at 652 km/h, and B flies on a course of 272 degrees at 546 km/h. Calculate their distance apart after 25 minutes to the nearest kilometer. Show ALL your work.
Just asking, what would the answer be.
This is so that I can check my work to see if I did it right. This would be very very helpful!!!!!!!!!
Thanks
the angle between the two courses is ... 272 - 81 = 191
... 360 - 191 = 169 ... this is the included angle
find the distances along the two courses ... distance = rate * time
you now have two sides of an obtuse triangle and the angle between them
use the Law of Cosines to find the 3rd side (the distance between the aircraft)
haven't solved it ... post a number and I'll be happy to check it
My answer was 497km. It would be great if you could check that for me
looks good
To find the distance between the two aircraft, we can use the Law of Cosines, which states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those sides and the cosine of the included angle.
Let's break down the problem into smaller steps:
Step 1: Convert 25 minutes to hours.
Since we need to find the distance after 25 minutes, we must convert this time into hours. There are 60 minutes in an hour, so 25 minutes is equal to 25/60 = 0.4167 hours.
Step 2: Determine the distance covered by each aircraft.
To calculate the distance covered by each aircraft, we will use the formula: Distance = Speed * Time.
For aircraft A:
Distance_A = Speed_A * Time = 652 km/h * 0.4167 h = 271.338 km (rounded to three decimal places).
For aircraft B:
Distance_B = Speed_B * Time = 546 km/h * 0.4167 h = 227.094 km (rounded to three decimal places).
Step 3: Convert the angle to radians.
The Law of Cosines requires the angle to be in radians. To convert degrees to radians, we use the formula: Radians = Degrees * (π/180).
For aircraft A:
Angle_A = 81° * (π/180) = 1.4137 radians (rounded to four decimal places).
For aircraft B:
Angle_B = 272° * (π/180) = 4.7454 radians (rounded to four decimal places).
Step 4: Calculate the distance between the two aircraft using the Law of Cosines.
The Law of Cosines formula is: c^2 = a^2 + b^2 - 2ab * cos(C).
c: Distance between the aircraft (what we're trying to find)
a: Distance covered by aircraft A
b: Distance covered by aircraft B
C: Angle between the two aircraft
Plugging in the values we calculated in previous steps:
c^2 = 271.338 km^2 + 227.094 km^2 - 2 * 271.338 km * 227.094 km * cos(4.7454 radians).
Step 5: Calculate the distance between the aircraft.
Now we need to take the square root of c^2 to find the actual distance.
c = sqrt(c^2).
Following this step, we calculate the value of c to the nearest kilometer to get the final answer.
Note: It's important to use a scientific calculator or a tool that can handle trigonometric functions and square roots for these calculations.
By following these steps and performing the necessary calculations, you should be able to find the distance between the two aircraft after 25 minutes.