Respuesta :
we know that
the law of cosines is equal to
[tex]a^{2} =b^{2} +c^{2}-2(b)(c)cos(A)[/tex]
In this problem for the triangle RST
we have
[tex]5^{2} =7^{2} +3^{2}-2(7)(3)cos(S)[/tex]
so
[tex]s=5[/tex]
[tex]r=7[/tex] or [tex]r=3[/tex]
[tex]t=3[/tex] or [tex]t=7[/tex]
the possibilities are
1) [tex]s=5[/tex]
[tex]r=7[/tex]
[tex]t=3[/tex]
2) [tex]s=5[/tex]
[tex]r=3[/tex]
[tex]t=5[/tex]
therefore
the answer is the option
s = 5 and t = 3
The law of cosine is the relationship between the sides of the triangle to the angle of the oblique triangle.
The value of [tex]s[/tex] is 5, value of [tex]t[/tex] is 3 and the value of [tex]r[/tex] is 7. Thus the option 4 is the correct option.
What is law of cosine?
The law of cosine is the nothing but the relationship between the sides of the triangle to the angle of the triangle (oblique triangle).
It can be given as,
[tex]a^2 = b^2 + c^2 - 2bc\cos(A)[/tex]
Here [tex](A)[/tex] is the angle of the triangle and [tex]a,b,c[/tex] are the sides of that triangle.
Given information-
The given law of cosine in the problem is,
[tex]5^2 = 7^2 + 3^2 - 2(7)(3)cos(S).[/tex]
Compare it with the above cosine law, we get,
[tex]s=5[/tex]
Now the value of [tex]r[/tex] and [tex]s[/tex] can be [tex]3[/tex] or [tex]7[/tex].
If the value of [tex]r[/tex] is 3 then the value of [tex]t[/tex] must be 7 and If the value of [tex]r[/tex] is 7 then the value of [tex]t[/tex] must be 3.
As [tex]s[/tex] is 5. Thus from the given option the best possibility is that [tex]t[/tex] should be 3.
Hence the value of [tex]s[/tex] is 5, value of [tex]t[/tex] is 3 and the value of [tex]r[/tex] is 7. Thus the option 4 is the correct option.
Learn more about the cosine law here;
https://brainly.com/question/4372174
