The value of RT is [tex]RT = \sqrt{306-270\cdot \cos \theta}[/tex], where collinearity exists for [tex]\theta = 180^{\circ}[/tex].
In this question, we do not know if [tex]\overline{RS}[/tex] and [tex]\overline {ST}[/tex] are Collinear, but we are certain that are Coplanar. In order to consider all scenarios, we shall make use of the property of the Sum of Internal Angles of Triangles equals 180°. and the Law of Cosine:
[tex]RT = \sqrt{RS^{2}+ST^{2}-2\cdot RS\cdot ST\cdot \cos S}[/tex], where [tex]0^{\circ}\le \theta \le 180^{\circ}[/tex] (1)
If we know that [tex]RS = 15[/tex] and [tex]ST = 9[/tex], then the value of [tex]RT[/tex] is described by the following expression:
[tex]RT = \sqrt{15^{2}+9^{2}-2\cdot (15)\cdot (9)\cdot \cos \theta}[/tex]
[tex]RT = \sqrt{306-270\cdot \cos \theta}[/tex], where collinearity exists for [tex]\theta = 180^{\circ}[/tex].
Please see this related question for further details: https://brainly.com/question/14273528
