Question

angle of triangle ABC where A = 90°, B = 30° and C = 60° where BC = 13 cm​

Answer 1

In a right triangle with one angle equal to 30 the side opposing this angle is half of the hypotenuse. If BC opposing this angle is 12 cm then the hypotenuse is 24 cm. Then AB (the other side) is sqrt(24^2–12^2)=20.78 cm (Pythagora). Then the right triangle's area = semi-product of the sides = (12*20.78)/2 = 124.71 cm^2

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Answer 2

Under the conditions you gave, trangle ABC is a 30, 60, 90 right triangle.with Angle A=30 and C=60.

So since triangle BDC has three 60 deg angles, it is an equalateral triangle with sides CD, BD and BC equal.

Triangle ABD is isoceles with angles ABD and BAD equal to 30 deg. So sides AD and BD are equal.