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

angles formed by these tosses are
`79.45, 59.02` and
`41.53` degrees to the nearest hundredth.

Explanation:

Here , We have a triangle with sides of length 8.6 feet, 5.8 feet and 7.5 feet.

The Law of Cosines (also called the Cosine Rule) says:

`c^2 = a^2 + b^2 - 2ab (cosx)`

Using the Cosine Rule to find the measure of the angle opposite the side of length 8.6 feet:

⇒
`c^2 = a^2 + b^2 - 2ab (cosx)`

⇒
`c^2 -a^2 - b^2 = -2ab (cosx)`

⇒
`(cosx) =( c^2 -a^2 - b^2)/( -2ab)`

⇒
`(cosx) =((8.6^2 - 5.8^2 - 7.5^2))/( ( -2(5.8)7.5))`

⇒
`(cosx) =0.18310`

⇒
`cos^(-1)(cosx) = cos^(-1)(0.18310)`

⇒
`x = 79.45`

The Law of Sines (or Sine Rule) is very useful for solving triangles:

`(a)/(sin A) = ( b)/(sin B) = (c)/(sin C)`

We can now find another angle using the sine rule:

⇒
`( 8.6 )/( sin 79.45) = (7.5)/( sin Y)`

⇒
`sin Y = ((7.5 (sin 79.45)))/( 8.6)`

⇒
`Y = 59.02 degrees`

So, the third angle =
`180 - 79.45 - 59.02 = 41.53 degrees.`

Therefore, angles formed by these tosses are
`79.45, 59.02` and
`41.53` degrees to the nearest hundredth.