two airways cross each other at an angle of 49 degrees. at a certain instant, the american airlines plane is 32 miles from the crossing, while the british airways plane is 76 miles from the crossing. what is the distance between the two planes at this ins -
To find the distance between the two planes, we can use the Law of Cosines.
The Law of Cosines states that in any triangle, the square of one side is equal to the sum of the squares of the other two sides, minus two times the product of the lengths of those sides, and the cosine of the included angle.
Let's assume that the distance between the two planes at a certain instant is represented by the letter "d".
Using the Law of Cosines, we can write the equation:
d^2 = 32^2 + 76^2 - 2 * 32 * 76 * cos(49°)
Now, let's solve this equation to find the distance "d" between the two planes.
First, calculate the value of cos(49°). You can use a calculator or lookup tables to find the cosine value. Let's assume it is approximately 0.647.
d^2 = 32^2 + 76^2 - 2 * 32 * 76 * 0.647
Now, simplify the equation:
d^2 = 1024 + 5776 - 3944.192
Combine the terms:
d^2 = 2855.808
Finally, take the square root of both sides to find the value of "d":
d ≈ √2855.808 ≈ 53.47 miles
Therefore, the distance between the two planes at this instant is approximately 53.47 miles.