In a right-angled triangle, one of the legs is 10, and the angle opposite it is 30 degrees. Find the square of the triangle.

1. Vertices of the triangle – A, B, C. AB = 10 units. ∠А = 90 °. ∠С = 30 °. S is the area of the triangle.

2. We calculate the length of the second leg AC through one of the trigonometric functions ∠C (tangent):

AB / AC = tangent ∠C = tangent 30 ° = √3 / 3.

AC = AB: √3 / 3 = 10: √3 / 3 = 10√3 units.

4. S = AB x AC: 2 = 10 x 10√3: 2 = 50√3 units².

Answer: S = 50√3 units of measurement².