In a right-angled triangle ABC, the hypotenuse BC = 6cm, AB = 3cm. what is the angle ABC?

1. Let us introduce the designation of the angle by the symbol ∠.

2. In this right-angled triangle, the leg AB has a length that is half the length of the hypotenuse BC (6 cm: 3 cm = 2) and is opposite ∠ACB. Therefore, according to the properties of a right-angled triangle, ∠ACB is equal to 30 °.

3. We calculate the value of the sought ∠ABC, taking into account that the total value of all angles of any triangle is 180:

∠ABС = 180 ° – ∠АСВ – ∠ВАС = 180 ° – 30 ° – 90 ° = 60 °.

Answer: ∠ABS is equal to 60 °.