In triangle ABC, it is known that ∠C = 90 °, AC = 10 cm, AB = 20 cm. Find the angle A of this triangle.

In a right-angled triangle ABC AB – hypotenuse; AC – leg;

AB = 20 cm; AC = 10 cm;

AC / AB = 10/20 = 1/2;

Therefore, the leg is equal to half of the hypotenuse.

If the leg in a right-angled triangle is two times smaller than the hypotenuse, then it lies opposite an angle of 30 °. The leg AC lies opposite the angle B, therefore <B = 30 °;

<A = 90 ° – <B; <A = 90 ° – 30 ° = 60 °.