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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.

Respuesta :

Answer:40.5 ft

Step-by-step explanation:

Given

[tex]\angle V=90^{\circ}[/tex]

[tex]\angle T=26^{\circ}[/tex]

[tex]VT=83\ ft[/tex]

from the figure we can write as

[tex]\tan 26^{\circ}=\dfrac{UV}{VT}[/tex]

[tex]\tan 26^{\circ}=\dfrac{UV}{83}[/tex]

[tex]\Rightarrow UV=83\times \tan 26^{\circ}[/tex]

[tex]\Rightarrow UV=40.48\ ft\approx 40.5\ ft[/tex]

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Answer:

Length of UV = 40.5 feet

Step-by-step explanation:

In the figure attached,

We will apply sine rule in ΔTUV,

[tex]\frac{SinT}{UV}=\frac{SinU}{TV}[/tex]

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,

[tex]\frac{Sin26}{UV}=\frac{Sin64}{83}[/tex]

UV = [tex](\frac{Sin26}{Sin64})\times 83[/tex]

UV = 40.48

     ≈ 40.5 feet

Therefore, length of UV will be 40.5 feet.

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