A plane leaves hamilton and flies due east 75 km at the same time a second plane flies in a direction of 40degress southeast for 120 km how far apart are the planes when they reach their destination.
I say the calculation is 75^2+120^2-2(75)(120)cos40
the book says to use cos 45 is this a typo or am I missing something???
I agree with you,
don't see how the angle of 45° can enter the picture.
I can see confusion about their "direction of 40° southeast"
- it could mean E 40° S, or
- it could mean S 40° E to some people.
but even with those interpretations the other angle would be 50°
To find the distance between the two planes when they reach their destination, we can use the Law of Cosines. However, there seems to be a confusion with the angles in the problem.
Let's break down the problem step by step:
1. The first plane flies due east for 75 km.
2. The second plane flies in a direction of 40 degrees southeast for 120 km.
To find the angle formed by the two planes at the common point, we need to subtract the given angle of 40 degrees from 180 degrees (a straight angle). Therefore, the angle formed is 180 - 40 = 140 degrees.
Now, using the Law of Cosines, we can calculate the distance between the two planes when they reach their destination, D:
D^2 = 75^2 + 120^2 - 2(75)(120) * cos(140)
The value of the cosine function depends on the angle given in degrees, not 45 degrees as mentioned in the book. So, using the correct angle of 140 degrees, let's calculate the value.
D^2 = 75^2 + 120^2 - 2(75)(120) * cos(140)
Now, we can solve this equation to find the value of D.
I hope this helps clarify the confusion about the calculation.