Segment AD perpendicular to the plane triangle ABC. It is known that AB = AC = 10 cm

Segment AD perpendicular to the plane triangle ABC. It is known that AB = AC = 10 cm, BC = 12 cm, and AD = 15 cm. Find the distance from point D to the side BC.

The shortest distance from point D to the side BC will be the perpendicular dropped from point D on the BC to the point that we will call E. We get a right-angled triangle ADE, in which we need to find the side AE first.

Consider triangle ABE, which is the mirror half of the equilateral triangle ABC. Hence:

BE = 1/2 BC = 6 cm.

AE ^ = AB ^ – BE ^ = 100 – 36 = 64.

AE = 8.

In triangle ADE, define the desired distance DE:

DE ^ = AD ^ + AE ^ = 225 + 64 = 289.

Answer: DE = 17 cm.