The length of the leg of a right-angled triangle is 12 cm, and the degree measure

The length of the leg of a right-angled triangle is 12 cm, and the degree measure of the angle adjacent to this leg is -30 degrees. Find the area of the triangle.

Let’s denote the second unknown leg through x, and the opposite angle is 30 °. Then one property can be applied: a leg that lies opposite an angle of 30 ° is equal to 1/2 of the hypotenuse. In our case – 2 * x.

Let’s use the Pythagorean theorem:

12 ^ 2 + x ^ 2 = (2 * x) ^ 2;

144 + x ^ 2 = 4 * x ^ 2;

144 = 4 * x ^ 2 – x ^ 2;

3 * x ^ 2 = 144;

x ^ 2 = 144: 3;

x ^ 2 = 48;

x = 4 * sqrt 3 (cm).

Find the area of the triangle:

S = 1/2 * 12 * 4 * sqrt 3 = 24 * sqrt 3 (cm).

Answer: 24 * sqrt 3 (cm).




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