The tree is at a distance of 5 steps from the 5 m high lantern, giving a shadow equal to 3 m. Find the height of the tree.

univerkov | February 7, 2021 | education

Determine the length of the segment AD. AD = AK + DK = 3 + 5 = 8 m.

Let us prove that the triangle AСD is similar to the triangle ABK.

Both triangles are straight, since СD and ВK are perpendicular to AD, and the angle A is common for the triangles, then the triangles are similar in acute angle.

СD / ВК = AD / AK.

5 / ВK = 8/3.

8 * ВK = 3 * 5.

8 * ВK = 15.

ВK = 15/8 = 1.875 m.

Answer: The length of the tree is 1.875 meters.

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