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

Answer:

Length of UV = 40.5 feet

Step-by-step explanation:

In the figure attached,

We will apply sine rule in ΔTUV,

$\frac{SinT}{UV}=\frac{SinU}{TV}$

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,

$\frac{Sin26}{UV}=\frac{Sin64}{83}$

UV = $(\frac{Sin26}{Sin64})\times 83$

UV = 40.48

     ≈ 40.5 feet

Therefore, length of UV will be 40.5 feet.

Answer 2

Answer:40.5 ft

Step-by-step explanation:

Given

$\angle V=90^{\circ}$

$\angle T=26^{\circ}$

$VT=83\ ft$

from the figure we can write as

$\tan 26^{\circ}=\dfrac{UV}{VT}$

$\tan 26^{\circ}=\dfrac{UV}{83}$

$\Rightarrow UV=83\times \tan 26^{\circ}$

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