In a right-angled triangle ABC, angle C = 90 *, angle A = 30 *, AC = 10 cm

In a right-angled triangle ABC, angle C = 90 *, angle A = 30 *, AC = 10 cm, CD-height drawn to side AB, DE- perpendicular drawn from point D to side AC. What is the length of AE?

In a right-angled triangle ADC, the angle A, by condition, is equal to 30, then the leg DC is equal to half the length of the AC, since it lies opposite the angle 30. DC = AC / 2 = 10/2 = 5 cm.

Consider a right-angled triangle CDE, in which the angle E = 90 by condition, and the angle CDE = ADC – ADE = 90 – 60 = 30, then the leg CE lies opposite the angle 30 and is equal to half the length of DC. CE = DC / 2 = 5/2 = 2.5 cm.

Then the segment AE = AC – CE = 10 – 2.5 = 7.5 cm.

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