Answer:
B
Step-by-step explanation:
The triangle RUS is similar to RST. 9/sqrt(90)=y/(3+x) and y^2=x^2+81. Solving all this will give x=27 and y=9*sqrt(10)
Value of x is 27 and value of y is [tex]9\sqrt{10}[/tex].
The angle addition postulate in geometry states that if we place two or more angles side by side such that they share a common vertex and a common arm between each pair of angles, then the sum of those angles will be equal to the total sum of the resulting angle.
X-value:
<RST = [tex]90^{0}[/tex]
[tex]tan( < RSU)= \frac{\overline R \overline U}{\overline S \overline U}[/tex]
[tex]tan( < RSU) = \frac{3}{9}[/tex]
[tex]< RSU = 18.435^{0}[/tex]
Angle addition postulate:
<RST = <RSU + <TSU
[tex]90^{0} =18.435^{0} + < TSU[/tex]
[tex]< TSU =71.565^{0}[/tex]
[tex]tan( < TSU) = \frac{\overline T \overline U }{\overline S \overline U}[/tex]
[tex]tan(71.565^{0})=\frac{x}{9}[/tex]
[tex]x=27[/tex]
Y-value:
<RST = [tex]90^{0}[/tex]
[tex]tan( < RSU)= \frac{\overline R \overline U}{\overline S \overline U}[/tex]
[tex]tan( < RSU) = \frac{3}{9}[/tex]
[tex]< RSU = 18.435^{0}[/tex]
Angle addition postulate:
<RST = <RSU + <TSU
[tex]90^{0} =18.435^{0} + < TSU[/tex]
[tex]< TSU =71.565^{0}[/tex]
[tex]cos( < TSU) = \frac{\overline S \overline U }{\overline S \overline T}[/tex]
[tex]cos(71.565^{0})=\frac{9}{y}[/tex]
[tex]y=9\sqrt{10}[/tex]
Value of x is 27 and value of y is [tex]9\sqrt{10}[/tex].
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