SOLUTION: A radar operator sights two objects, one a t a distance of 7 miles and the other at a distance of 12 miles. If the angle between the sightings is 35deg, how far apart are the objec

Algebra ->  Trigonometry-basics -> SOLUTION: A radar operator sights two objects, one a t a distance of 7 miles and the other at a distance of 12 miles. If the angle between the sightings is 35deg, how far apart are the objec      Log On


   

Question 70998: A radar operator sights two objects, one a t a distance of 7 miles and the other at a distance of 12 miles. If the angle between the sightings is 35deg, how far apart are the objects?
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You could use the law of cosines to solve this problem since you have two sides of a triangle and the included angle. Let the two known sides be a (12 miles) and b (7 miles). You want to find the length of the third side (c). The included angle is C = 35 degrees. The law of cosines is:
c%5E2+=+a%5E2%2Bb%5E2-2abcos%28C%29 Substituting the given values of a(12), b(7), and angle C(35):
c%5E2+=+12%5E2+%2B+7%5E2+-+2%2812%29%287%29cos%2835%29 Simplify.
c%5E2+=+144+%2B+49+-+168cos%2835%29
c%5E2+=+193+-+168%280.82%29
c%5E2+=+193-137.62
c%5E2+=+55.38 Take the square root of both sdes.
c+=+7.44
The two objects are approximately 7.44 miles apart.