# A ball is tossed between three friends. The first toss is 8.6 feet, the second is 5.8 feet, and the

###### Question:

## Answers

angles formed by these tosses are [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.

Step-by-step 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:

[tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]

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

⇒ [tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]

⇒ [tex]c^2 -a^2 - b^2 = -2ab (cosx)[/tex]

⇒ [tex](cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}[/tex]

⇒ [tex](cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}[/tex]

⇒ [tex](cosx) =0.18310[/tex]

⇒ [tex]cos^{-1}(cosx) = cos^{-1}(0.18310)[/tex]

⇒ [tex]x = 79.45[/tex]

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

[tex]\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}[/tex]

We can now find another angle using the sine rule:

⇒[tex]\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}[/tex]

⇒[tex]sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}[/tex]

⇒[tex]Y = 59.02 degrees[/tex]

So, the third angle =[tex]180 - 79.45 - 59.02 = 41.53 degrees.[/tex]

Therefore, angles formed by these tosses are [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.

angles formed by these tosses are [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.

Step-by-step 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:

[tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]

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

⇒ [tex]c^2 = a^2 + b^2 - 2ab (cosx)[/tex]

⇒ [tex]c^2 -a^2 - b^2 = -2ab (cosx)[/tex]

⇒ [tex](cosx) =\frac{ c^2 -a^2 - b^2}{ -2ab}[/tex]

⇒ [tex](cosx) =\frac{(8.6^2 - 5.8^2 - 7.5^2)}{ ( -2(5.8)7.5)}[/tex]

⇒ [tex](cosx) =0.18310[/tex]

⇒ [tex]cos^{-1}(cosx) = cos^{-1}(0.18310)[/tex]

⇒ [tex]x = 79.45[/tex]

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

[tex]\frac{a}{sin A} = \frac{ b}{sin B} = \frac{c}{sin C}[/tex]

We can now find another angle using the sine rule:

⇒[tex]\frac{ 8.6 }{ sin 79.45} = \frac{7.5}{ sin Y}[/tex]

⇒[tex]sin Y = \frac{(7.5 (sin 79.45))}{ 8.6}[/tex]

⇒[tex]Y = 59.02 degrees[/tex]

So, the third angle =[tex]180 - 79.45 - 59.02 = 41.53 degrees.[/tex]

Therefore, angles formed by these tosses are [tex]79.45, 59.02[/tex] and [tex]41.53[/tex] degrees to the nearest hundredth.

The angles are 79.45, 59.02 and 41.53 degrees to the nearest hundredth.

Step-by-step explanation:

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

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

cos X = (8.6^2 - 5.8^2 - 7.5^2) / ( -2*5.8*7.5)

= 0.18310

X = 79.45 degrees.

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.

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°