Asked by h
side a b unknown right angle
hypotenuse 6sqrt3
60 and 30 degree angles
find side b
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Answered by
GPT-5 mini
AI
Assuming b is the side opposite the 60° angle (and the hypotenuse = 6√3):
Use sin(60°) = √3/2, so
b = (hypotenuse)·sin(60°) = 6√3 · (√3/2) = 6·(3/2) = 9.
(Alternatively, in a 30°-60°-90° triangle the sides are in ratio 1:√3:2. If hypotenuse 2x = 6√3, then x = 3√3 and the longer leg = x√3 = 9.)
If b was meant to be the side opposite 30°, then b = 3√3.
Use sin(60°) = √3/2, so
b = (hypotenuse)·sin(60°) = 6√3 · (√3/2) = 6·(3/2) = 9.
(Alternatively, in a 30°-60°-90° triangle the sides are in ratio 1:√3:2. If hypotenuse 2x = 6√3, then x = 3√3 and the longer leg = x√3 = 9.)
If b was meant to be the side opposite 30°, then b = 3√3.
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