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Lesechka [4]
3 years ago
13

In ΔTUV, t = 410 cm, ∠U=27° and ∠V=78°. Find the length of v, to the nearest 10th of a centimeter.

Mathematics
1 answer:
telo118 [61]3 years ago
6 0

Answer:

v \approx 415.2\,cm

Step-by-step explanation:

The angle T is:

\angle T = 180^{\circ} - 27^{\circ} - 78^{\circ}

\angle T = 75^{\circ}

Now, the length of v is determine by the Law of Sines:

\frac{410\,cm}{\sin 75^{\circ}} = \frac{v}{\sin 78^{\circ}}

v = (410\,cm)\cdot \left(\frac{\sin 78^{\circ}}{\sin 75^{\circ}} \right)

v \approx 415.2\,cm

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