Given:
Given that ΔTUV is a right triangle. The measure of ∠V=90°, the measure of ∠U=55°, and VT = 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], [tex]opp=82[/tex] and [tex]hyp =TU[/tex]
Substituting the values, we get;
[tex]sin \ 55^{\circ}=\frac{82}{TU}[/tex]
Simplifying, we get;
[tex]TU=\frac{82}{sin \ 55^{\circ}}[/tex]
[tex]TU=\frac{82}{0.819}[/tex]
[tex]TU=100.12[/tex]
Rounding off to the nearest tenth, we get;
[tex]TU=100.1[/tex]
Thus, the length of TU is 100.1 feet.
