Answer :

DavisLaurant

Since sinU is opposite over hypotenuse, it would equal VT/52

We can figure out VT with the Pythagorean Theorem.

VT=[tex]\sqrt{52^2-20^2[/tex]

Simplify and substitute into the fraction

      =[tex]\sqrt{2704-400}= 48[/tex]  ---> [tex]\frac{48}{52}[/tex]

I'll let you reduce. If this helped, please mark me as Brainliest. Good luck!

msm555

Answer:

[tex] \sf \sin(U) = \dfrac{{12}}{{13}}[/tex]

Step-by-step explanation:

To find the sine of ∠ U in triangle \triangle UTV, we use the definition of sine:

[tex] \Large\boxed{\boxed{\sf \sin(U) = \dfrac{{\textsf{Opposite}}}{{\textsf{VT}}}}}[/tex]

[tex] \sf \sin(U) = \dfrac{{\textsf{Opposite}}}{{\textsf{UV}}} [/tex]

Given:

  • Adjacent side (UT)) = 20,
  • Hypotenuse (UV)) = 52.

We need to find the length of the opposite side (VT). Using the Pythagorean theorem:

[tex] \sf UV^2 = UT^2 + VT^2[/tex]

[tex] \sf 52^2 = 20^2 + VT^2[/tex]

[tex] \sf 2704 = 400 + VT^2[/tex]

[tex] \sf VT^2 = 2704 - 400[/tex]

[tex] \sf VT^2 = 2304[/tex]

[tex] \sf VT = \sqrt{2304}[/tex]

[tex] \sf VT = 48[/tex]

Now, substitute the values into the formula for sine:

[tex] \sf \sin(U) = \dfrac{{48}}{{52}}[/tex]

[tex] \sf \sin(U) = \dfrac{{48 \div 4}}{{52 \div 4}}[/tex]

[tex] \sf \sin(U) = \dfrac{{12}}{{13}}[/tex]

So, the sine of ∠ U is 12/13.