In a right-angled triangle abc, angle c = 90 degrees, angle a = 30 degrees

In a right-angled triangle abc, angle c = 90 degrees, angle a = 30 degrees, AC = 10 cm, CD perpendicular to side AB, DE perpendicular to side AC. Find AE.

Since CD is perpendicular to AB, then triangle ACD is rectangular in which the leg CD lies opposite angle 30, then CD = AC / 2 = 10/2 = 5 cm.

DE perpendicular to AC, then triangle CDE is rectangular, in which the angle ECD = 60, and the angle CDE = 90 – 60 = 30.

The CE leg lies against an angle of 30, then CE = CD / 2 = 5/2 = 2.5 cm.

AE = AC – CE = 10 – 2.5 = 7.5 cm.

Answer: The length of the segment AE is 7.5 cm.