Question

A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet , and the third toss is 7.5 feet, which takes the ball back to the starting point. What angles are formed by these tosses..Step by step explanation ..Please

Answer 1

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:

$cos x = \frac{(8.6)^2 - (5.8)^2 - (7.5)^2}{-2 X 5.8 X 7.5} \\\\cosx = 0.18310\\\\x = 79.45$

We can now find another angle using the sine rule:

$\frac{8.6}{sin 79.45} = \frac{7.5}{siny} \\\\sin y = \frac{7.5 X sin 79.45}{8.6} \\\\y = 59.02$

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°