Question

Two goals post are 8m apart. A footballer is 34m from one and 38m from the other. Within what angle must he kick the ball if he is to score a goal?​

Answer 1

11.06°

Explanation:

The law of cosines can be used to find the angle. The sides adjacent to that angle are a=34, b=38, and the side opposite is c=8. Then the angle is found from ...

c² = a² +b² -2ab·cos(C)

cos(C) = (a² +b² -c²)/(2ab)

C = arccos((a² +b² -c²)/(2ab))

C = arccos((34² +38² -8²)/(2·34·38)) = arccos(317/323)

C ≈ 11.06°

From the footballer's viewpoint, the goal posts are 11.06° apart.