Question

the side opposite the right angle measures 8 in. what is the measurement of the side opposite of the 60 degree angle (draw and label the triangle before solving)

Answer 1

`4\sqrt[]{3}`

1) The best way to tackle this question is by sketching out the triangle:

2) Considering that 60º angle we can write out the following trig ratio:

`\begin{gathered} \sin (60^(\circ))=(x)/(8) \\ \frac{\sqrt[]{3}}{2}=(x)/(8) \\ 2x=8\sqrt[]{3} \\ x=\frac{8\sqrt[]{3}}{2} \\ x=4\sqrt[]{3} \end{gathered}`

Note that if we had drawn the 60º angle to the lowe right in that triangle we would find the same measure, by using the cosine of (30º) instead.

And that's the answer