The measurements of missing angles and sides is:
ST = [tex]3\sqrt{55}[/tex], [tex]\angle T = 22.02^\circ[/tex], and [tex]\angle R = 67.96^\circ[/tex].
Given that:
Triangle RST is right angled triangle.
Side RT = Hypotenuse = of 24 units
Side SR = 9 units
Calculations of angle R and T and length of ST:
By Pythagoras Theorem:
[tex]ST^2 + RS^2 = RT^2\\\\ST = \sqrt{RT^2 - RS^2}\\\\ST = \sqrt{24^2 - 9^2}\\\\ST = \sqrt{495} = 3\sqrt{55}[/tex]
Let angle T = [tex]\theta[/tex], then:
[tex]sin(T) = \dfrac{9}{24}\\\\T = arcsin{0.375}\\\\T = 22.02^\circ[/tex]
Since sum of all triangles is 180 degrees, thus:
[tex]\angle S + \angle T + \angle R = 180^\circ\\\angle R = 180 - 90 - 22.04 = 67.96^\circ[/tex]
Thus, ST = [tex]3\sqrt{55}[/tex], [tex]\angle T = 22.02^\circ[/tex], and [tex]\angle R = 67.96^\circ[/tex].
Learn more about right angled triangles here:
https://brainly.com/question/3770177
