Question

1. A 30-60-90 triangle has a hypotenuse of 10. Use trig (sine, cosine, or tangent) to find the short side. Show your work.

Answer 1

Given the right triangle:

Where a is the short side. Then, using the definition of the sine function:

$\sin30\degree=\frac{a}{10}$

But we know that:

$\sin30\degree=\frac{1}{2}$

Finally:

$\begin{gathered} \frac{1}{2}=\frac{a}{10} \\ \\ \Rightarrow a=\frac{10}{2} \\ \\ \therefore a=5 \end{gathered}$