Given:
Given that TUV is a right triangle with measure of ∠V=90°
The measure of ∠U = 55°, and the length of VT is 82 feet.
We need to determine the length of TU.
Length of TU:
The length of TU can be determined using the trigonometric ratio.
Thus, we have;
[tex]sin \ \theta=\frac{opp}{hyp}[/tex]
where [tex]\theta=55^{\circ}[/tex], opp = VT and hyp = TU
Thus, we have;
[tex]sin \ 55^{\circ}=\frac{VT}{TU}[/tex]
Substituting the values, we have;
[tex]sin \ 55^{\circ}=\frac{82}{TU}[/tex]
Simplifying, we have;
[tex]TU=\frac{82}{sin \ 55^{\circ}}[/tex]
[tex]TU=\frac{82}{0.819}[/tex]
[tex]TU=100.1[/tex]
Thus, the length of TU is 100.1 feet.
