Question

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.

Answer 1

Length of UV = 40.5 feet

Explanation:

In the figure attached,

We will apply sine rule in ΔTUV,

`(SinT)/(UV)=(SinU)/(TV)`

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,

`(Sin26)/(UV)=(Sin64)/(83)`

UV =
`((Sin26)/(Sin64))* 83`

UV = 40.48

≈ 40.5 feet

Therefore, length of UV will be 40.5 feet.

Answer 2

Answer:40.5 ft

Explanation:

Given

`\angle V=90^(\circ)`

`\angle T=26^(\circ)`

`VT=83\ ft`

from the figure we can write as

`\tan 26^(\circ)=(UV)/(VT)`

`\tan 26^(\circ)=(UV)/(83)`

`\Rightarrow UV=83* \tan 26^(\circ)`

`\Rightarrow UV=40.48\ ft\approx 40.5\ ft`