The lantern illuminates a tree with a height of 2.8 m, located at a distance of 6 m from the negon
| April 9, 2021 | education
The lantern illuminates a tree with a height of 2.8 m, located at a distance of 6 m from the negon, the length of the shadow cast by this tree is 4 m. At what height does the lantern hang?
Determine the length of the segment AD. AD = AK + DK = 4 + 6 = 10 m.
Let us prove that triangle ACD is similar to triangle ABK.
Both triangles are straight, since CD and BK are perpendicular to AD, and the angle A is common for the triangles, then the triangles ACD and ABK are similar in acute angle.
CD / BK = AD / AK.
CD / 2.8 = 10/4.
4 * CD = 2.8 * 10.
4 * AD = 28.
AD = 28/4 = 7 m.
Answer: The lantern hangs at a height of 7 meters.
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