Respuesta :
Answer:[tex]c=\sqrt{19}[/tex]
Step-by-step explanation
Two sides and included angle is known to us .cosine rule can be applied to find the third side.
Let a =2 ,b=5 and <C=60 degrees ,we need to find the third side c.
According to cosine rule :
[tex]c^{2} =a^{2} +b^{2} -2abcos C.[/tex]
Substituting the values we have:
[tex]c^{2}=2^{2} +5^{2} -2(2)(5)cos 60[/tex]
[tex]c^{2} =4+25-20 (\frac{1}{2} )[/tex]
[tex]c^{2} =29-10=19[/tex]
Taking root of both sides
[tex]c=\sqrt{19}[/tex]
The last option is correct.
