Question

The hypotenuse of a 30°-60°-90° triangle measures 32 in. What is the length of the shorter leg?

Answer 1

now according to the angles...

the shortest side is "b" and we can find it by using sin of 30 degrees

\[\LARGE \sin30^{\circ}=\frac{b}{c}\]
since..
\[\LARGE \sin30^{\circ}=\frac12\]

we have:

\[\LARGE \frac12=\frac{b}{32}\]

\[\LARGE 2b=32 \Longrightarrow b=\frac{32}{2} \longrightarrow b=16\]