In a right-angled triangle abc, angle c right angle b 30 degrees hypotenuse ab 16 cm.

In a right-angled triangle abc, angle c right angle b 30 degrees hypotenuse ab 16 cm. Find the area of the triangle.

Since we know that the triangle ABC is rectangular, and the angle ABC = 30 °, then opposite the angle of 30 ° lies the leg AC, equal to half of the hypotenuse AB.

Then we get that AC = 1/2 * AB = 1/2 * 16 = 8 cm.

Since the triangle ABC is right-angled, we will use the Pythagorean theorem for a right-angled triangle:

AB ^ 2 = AC ^ 2 + CB ^ 2;

CB ^ 2 = AB ^ 2 – AC ^ 2;

CB ^ 2 = 16 ^ 2 – 8 ^ 2;

CB ^ 2 = 256 – 64;

CB ^ 2 = 192;

CB = √192 = √ (16 * 12) = 4 * √ (4 * 3) = 4 * 2 * √3 = 8 * √3.

We find the area of a right-angled triangle by the formula:

S = (8 * √3 * 8) / 2 = (64 * √3) / 2 = 32 * √3.

Answer: 32 * √3.