Question

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

Answer 1

`v \approx 415.2\,cm`

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:

`(410\,cm)/(\sin 75^(\circ)) = (v)/(\sin 78^(\circ))`

`v = (410\,cm)\cdot \left((\sin 78^(\circ))/(\sin 75^(\circ)) \right)`

`v \approx 415.2\,cm`