Answer:
[tex]\cos(T)[/tex] =[tex]\frac{\sqrt{15}}{5}[/tex]
Step-by-step explanation:
Given parameters.
[tex]TU = 4\sqrt 5[/tex]
[tex]SU = 4\sqrt 2[/tex]
[tex]ST = 4\sqrt 3[/tex]
Required
Determine [tex]\cos(T)[/tex]
Reference to [tex]\angle T[/tex], we have:
[tex]Opposite = 4\sqrt 2[/tex]
[tex]Adjacent = 4\sqrt 3[/tex]
[tex]Hypotenuse = 4\sqrt 5[/tex]
Apply trigonometry ratio of cosine
[tex]\cos(T)[/tex] [tex]= \frac{Adjacent}{Hypotenuse}[/tex]
Substitute values for Adjacent and Hypotenuse
[tex]\cos(T)[/tex] [tex]= \frac{4\sqrt 3}{4\sqrt 5}[/tex]
[tex]\cos(T)[/tex] [tex]= \frac{\sqrt 3}{\sqrt 5}[/tex]
Rationalize:
[tex]\cos(T)[/tex] [tex]= \frac{\sqrt 3}{\sqrt 5}*\frac{\sqrt 5}{\sqrt 5}[/tex]
[tex]\cos(T)[/tex] =[tex]\frac{\sqrt{15}}{5}[/tex]
