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

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) (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:
Substituting the given values of a(12), b(7), and angle C(35):
Simplify.

Take the square root of both sdes.

The two objects are approximately 7.44 miles apart.
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