In a right-angled triangle ABC with a hypotenuse AB, the height CH is drawn. find HA if angle B = 60 °, BH = 2 cm.

1. In a right-angled triangle CBN, the height of CH is the leg opposite the angle

B equal to 60 °. The tangent of this angle is equal to the quotient of dividing CH by BH and is equal to √3.

With this in mind, we calculate the length of the CH height:

CH: BH = √3.

CH = 2 x √3 = 2√3 cm.

2. We calculate the value of the angle A:

angle A = 180 ° – 90 ° – 60 ° = 30 °.

3. The tangent of this angle is equal to the quotient of dividing CH by AH and is equal to √3 / 3.

4. Calculate the length of the segment AH:

CH: AH = √3 / 3.

AH = CH: √3 / 3 = 2√3: √3 / 3 = 6 cm.

Answer: the length of the segment AH is 6 cm.