Question

in triangle abc a =60 degree b=90degree c=30 degree and ac=6cm find the length of side ab

Answer 1

$\frac{1}{2} ac = ab \\ \frac{1}{2} \times 6 = 3 \\ ab = 3cm$
Converse of 30°-60°-90° theorem.
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Answer 2

Given that

AC = 6cm = Hypotenuse

< ACB = 30°

We can use Sin 30° = AB / AC ..... (1)

Sin 30 ° = 1/2 .....(2)

From (1) & (2)

$\frac{AB}{6} = \frac{1}{2} \\ \\ AB = \frac{6}{2} \\ \\ AB = 3cm$