The length of the shadow of a tree is 21 m. At the same time of day, the shadow of a person 1.8 m
| March 5, 2021 | education
The length of the shadow of a tree is 21 m. At the same time of day, the shadow of a person 1.8 m in height is 2.7 m. What is the height of the tree?
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 are similar in acute angle.
CD / BK = AD / AK.
CD / 1.8 = 21 / 2.7.
2.7 * CD = 21 * 1.8.
2.7 * CD = 37.8.
CD = 37.8 / 2.7 = 14 m.
Answer: The height of the tree is 14 meters.
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