A man with a height of 1.5 m stands at a distance of 12 m from the post, on the top of which there is a lantern.

A man with a height of 1.5 m stands at a distance of 12 m from the post, on the top of which there is a lantern. Find the height of the pillar if the length of the shadow cast by this person is 3 m.

Let us prove that triangle ACD is similar to triangle ABK.

Both triangles have a common angle A, and both triangles are right-angled, since CD and BK are parallel to AD, then the right-angled triangles ACD and ABK are similar in the first sign of similarity – in an acute angle.

Determine the length of the segment AD.

AD = AK + DK = 3 + 12 = 15 meters.

Then CD / BK = AD / AK.

CD / 1.5 = 15/3.

3 * CD = 1.5 * 15.

CD = 22.5 / 3.

CD = 7.5 m.

Answer: The height of the pillar is 7.5 meters.