The condition is not given to us completely, it should sound like this: we need to find the area of a right-angled triangle, the hypotenuse of which is 16 cm, and it is also known that one of the acute angles is 30 degrees.
Let’s find first of all one of the legs. It is known that a leg lying opposite an angle of 30 degrees is equal to half of the hypotenuse.
So, one of the legs is 16/2 = 8 cm.
We find the second leg by the Pythagorean theorem:
c ^ 2 = a ^ 2 + b ^ 2;
a = √ (c ^ 2 – b ^ 2) = √ (256 – 64) = √192 = 8√3 cm.
We find the area as half of the product of the legs:
S = 1 / 2ab = 1/2 * 8 * 8√3 = 32√3 cm ^ 2.
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