Andrea, Kim and Joy are attemptingto triangulate the locations of their homes for a science and math project. Kim lives 12 blocks away from andrea, Joy lives 7 blocks away from Kim and Andrea lives 15 blocks away from Joy.
a. imagine that the houses are in a triangle, and assume that Kim lives the farthest north, Andrea lives the farthest west and Joy lives the farthest east.
find the angles for each part of the triangle
+23251 Label the vertices of the triangle K (Kim), A (Andrea), and J (Joy).
The lengths of the sides of the triangles are: AK = 12, AJ = 15, and KJ = 7.
Since you know the three sides of the triangle, use the Law of Cosines: c2 = a2 + b2 - 2·a·b·cos(C).
To find angle K: AJ2 = AK2 + KJ2 - 2·AK·KJ·cos(K)
---> 152 = 122 + 72 - 2·12·7·cos(K)
---> 225 = 144 + 49 - 168·cos(K)
---> 225 = 193 - 168·cos(K)
---> 32 = -168·cos(K)
---> -32/168 = cos(K)
---> K = cos-1(-32/168)
---> K = 101º (approximately)
To find angle J: AK2 = AJ2 + KJ2 - 2·AJ·KJ·cos(J) (or you can use the Law of Sines)
---> 122 = 152 + 72 - 2·15·7·cos(J)
---> 144 = 225 + 49 - 210·cos(J)
---> 144 = 274 - 210·cos(J)
---> -130 = -210·cos(J)
---> 130/210 = cos(J)
---> J = cos-1(130/210)
---> J = 52º (approximately)
Thus A = 27º (approximately)
