In a right-angled triangle from the vertex of an angle equal to 60 degrees, a bisector is drawn

In a right-angled triangle from the vertex of an angle equal to 60 degrees, a bisector is drawn, the length of which is 22 cm. Find the length of the leg that lies opposite this angle.

Let’s designate our triangle ABC, angle A is a straight line, angle C = 60 °, CK is a bisector equal to 22 cm.
Consider a right-angled triangle AK, in it the leg AK is located opposite the angle KCA = 30 °, which means that it is equal to half the hypotenuse.
AK = 1/2 * SC = 1/2 * 22 = 11 (cm).
Consider a triangle BKC, it is isosceles (two angles are equal):
KВC angle = 90 ° – ACB angle = 90 ° – 60 ° = 30 °.
Angle KСВ = 30 ° (СK – bisector by condition).
The BKC triangle is isosceles, therefore, BK = CK = 22 (cm).
Let’s find the AB leg.
AB = AK + ВK = 11 + 22 = 33 (cm).
Answer: 33 centimeters.