In a right-angled triangle ABC with a hypotenuse AB, the height CH is drawn.

In a right-angled triangle ABC with a hypotenuse AB, the height CH is drawn. Find HA if the angle is B = 60 degrees, BH = 10 cm.

1. We calculate the length of the CH height through the tangent of angle B, the value of which is equal to the quotient of dividing the length of the CH leg by the length of the ВН leg of the right-angled triangle BCH:

CH: BH = tangent 60 °.

CH = BH x √3 = 10√3 centimeters.

2. We calculate the length of the segment AH using the formula for calculating the height drawn from the vertex of an angle equal to 90 °:

CH = √AН x BH.

CH ^ 2 = AH x BH.

AH = CH ^ 2: BH = (10√3) ^ 2: 10 = 300: 10 = 30 centimeters.

Answer: the length of the segment AH is 30 centimeters.