Question

How would go about finding the lengths of the longer leg and hypotenuse of a 30-60-90 triangle if the shorter leg was 10 ft.?

Answer 1

you can use sin cos or tan to find both depending on where the shortest leg is and which side it is that you're trying to find.

Answer 2

SOH CAH TOA

sin = opposite/hypotenuse
cos = adjacent/hypotenuse
tan = opposite/adjacent

The opposite and adjacent refer to the lengths.