Respuesta :
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.
