Answer:
See attached picture
Step-by-step explanation:
The ratios of sides in a 30°-60°-90° triangle are ...
... 1 : √3 : 2
Multiplying these ratio units by 3 inches, we get the side lengths to be ...
... 3 in : 3√3 in : 6 in
Thus, a = 3 in; b = 3√3 in.
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Alternate solution
Or, you can work from your memorized values of the trig functions of 30° and 60°.
... sin(30°) = a/(6 in) = 1/2 . . ⇒ . . a = (1/2)·6 in = 3 in
... cos(30°) = b/(6 in) = (√3)/2 . . ⇒ . . b = (√3)/2·6 in = 3√3 in
