In a right-angled triangle ABC, the hypotenuse AB is 44 cm, the angle B is 30 ‘. CH is the height of the triangle Find the segments BH and AH

Given:
right triangle ABC
angle C = 90 degrees
CH – height
AB = 4 cm
angle B = 30 degrees.
Find the lengths of the segments ВН, АН -?
Decision:
1. Consider a right-angled triangle ABC.
In a right-angled triangle opposite an angle of 30 degrees lies a leg, which is half the hypotenuse. Then BC = 1/2 * AB = 1/2 * 44 = 22 cm.
2. In a right-angled triangle, each leg is the average proportional between the hypotenuse and the projection of this leg onto the hypotenuse.
Then BC = √ (AB * HB);
22 = √ (44 * HB;
484 = 44 * HB;
HB = 484: 44;
HB = 11 cm.
3. So AH = AB – HB = 44 – 11 = 33 (cm).
Answer: 11 centimeters; 33 centimeters.