The angles formed by the tosses are 79.45°, 59.02° and 41.53°
Explanation:
The three different tosses form a triangle with three different sides.
We have a triangle with sides of length 8.6, 5.8 and 7.5 feet.
Let x°, y° and z° be the three angles of a triangle
Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:
[tex]cos x = \frac{(8.6)^2 - (5.8)^2 - (7.5)^2}{-2 X 5.8 X 7.5} \\\\cosx = 0.18310\\\\x = 79.45[/tex]
We can now find another angle using the sine rule:
[tex]\frac{8.6}{sin 79.45} = \frac{7.5}{siny} \\\\sin y = \frac{7.5 X sin 79.45}{8.6} \\\\y = 59.02[/tex]
So the third angle would be
z = 180 - 79.45 - 59.02
z = 41.53°
Therefore, the three angles are 79.45°, 59.02° and 41.53°
