In a open field, there are 5 christmas trees decorated with colors.
The red christmas tree and the orange christmas tree are 10 yards apart.
The yellow christmas tree is 12 yards from the red christmas tree. The
blue christmas tree is 14 yards from the orange tree. The pink christmas tree
is 17 yards from the blue christmas tree. The yellow christmas tree and
the orange christmas tree are 9 yards apart. The yellow christmas tree and
the pink christmas tree are 13 yards apart. The pink christmas tree and the
orange christmas tree are 11 yards apart. How far is is blue christmas
tree from the red christmas tree (rounded to the nearest yard)?
This problem may be solved using the cosine law for triangles,
which is.
a^{2} = b^{2} + c^{2}  2 b c cos(A)
where a, b, and c are the length of the sides of the triangle, and
angle A is the angle opposite side A.
The problem can be drawn into a diagram as follows
Solving for angle ROY, we let a=10, b=9, and c = 12, and
angle ROY is 78.1 degrees.
Solving for angle POY, we let a=11, b=9, and c = 13,
and angle POY is 80.4 degrees.
Solving for angle POB, we let a=11, b=14, and c = 17,
and angle POB is 84.8 degrees.
Angle ROB is therefore 360angle ROY angle
POY  angle POB and is 116.7
Solving for distance RB, we let b=10, c=14,
and A=angle ROB, and we get distance RB as 20.54
So the distance between the RED tree and the
Blue tree is approximately 21 yards.
