At any right angle, the sum of the 2 acute angles is 90 degrees
Then the 2 acute angles are complementary
sin one of the angle = cos the other angle
cos one of the angle = sin the other angle
From the figure, we can see
Triangle UVT is a right angle at V
Then v is the hypotenuse, u and t are the legs od the right angle
Now, let us answer the questions
Part (1):
[tex]\begin{gathered} \sin T=\frac{\text{opposite}}{\text{hypotenuse}} \\ \sin T=\frac{t}{v} \end{gathered}[/tex][tex]\begin{gathered} \cos T=\frac{adjacent}{\text{hypotenuse}} \\ \cos T=\frac{u}{v} \end{gathered}[/tex][tex]\begin{gathered} \sin U=\frac{opposite}{hypotenuse} \\ \sin U=\frac{u}{v} \end{gathered}[/tex][tex]\begin{gathered} \cos U=\frac{adjacent}{\text{hypotenuse}} \\ \cos U=\frac{t}{v} \end{gathered}[/tex]Part (2):
Since [tex]m\angle T+m\angle U=90^{\circ}[/tex]complementary
Part (3):
The correct statements are
[tex]\begin{gathered} \cos T=\sin U\rightarrow1st \\ \sin T=\cos U\rightarrow3rd \end{gathered}[/tex]Part (4):
Since cos a= sin b, then
a + b = 90 degrees
To find the missing angle subtract 73 from 90
[tex]90-73=17[/tex]Then the answer is
[tex]\cos (73^{\circ})=\sin (17^{\circ})[/tex]