In ΔTUV, the measure of ∠V=90°, the measure of ∠T=26°, and VT = 83 feet. Find the length of UV to the nearest tenth of a foot.

40.5 ft

Step-by-step explanation:

Given

from the figure we can write as

Length of UV = 40.5 feet

Step-by-step explanation:

In the figure attached,

We will apply sine rule in ΔTUV,

m∠T + m∠V + m∠U = 180°

26° + 90° + m∠U = 180°

m∠U = 180 - 116

m∠U = 64°

Now we put the values in sine rule,

UV =

UV = 40.48

     ≈ 40.5 feet

Therefore, length of UV will be 40.5 feet.