In a right-angled triangle ABC with a hypotenuse AB, the bisector BL is 2 times greater than CL

In a right-angled triangle ABC with a hypotenuse AB, the bisector BL is 2 times greater than CL and 17 cm less than AC. Find the larger leg of triangle ABC.

Since in a right-angled triangle BCL the hypotenuse BL is twice as large as the leg CL, then the angle CBL = 300, then the angle ABC = 2 * 30 = 60.

In a right-angled triangle ABC, the angle BAC = (90 – 60) = 30.

Then in triangle ABL the angles at the base of AB are equal to 30, therefore, triangle ABL is isosceles, AL = BL.

By condition, AC – BL = 17 cm, then (AL + CL) – BL = 17.

CL = 17 cm.

Then, BL = AL = 2 * CL = 2 * 17 = 34 cm.

AC = AL + CL = 34 + 17 = 51 cm.

Answer: The length of the larger leg is 51 cm.