Question

Barrie has buried his math treasure and two groups of students are trying to find it. Group A is 12.3km from the treasure. Group B is 16.4km from the treasure. If the angle that the treasure makes between group A and B is 57 degrees, how far apart are group A and B?

Answer 1

Answer:

14.2 km.

Step-by-step explanation:

That's a standard application of Al-Kashi law of cosines (or Carnot theorem, depends on how your book presents it)

Let's call x the distance between the group, and a and b the distance from each group from the Treasure.

$x^2=a^2+b^2-2ab\cdot cos57 =\\12.3^2 + 16.4^2 -2(12.3)(16.4)(0.544) \approx 200.52\\x= \sqrt {200.52} \approx14.2 km$

Obviously it's a distance so we take the positive value of the square root.