at a certain time of the day a tree casts its shadow 12.5 feet long . if the height of the is 5 feet. find the height of another tree that casts its shadow 20 feet long at the same time
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they both forms the similar triangles
let the triangle be ABC and DEF
in triangle ABC and DEF
one angle is 90° in both triangles
& one angle is formed by the sun which is equal in both triangles because they form shadows at same time
therefore
Both triangles are similar by AA similarity
so there corresponding sides are proportional
AB/DE = BC/EF [AB and DE are heights of
[tree and BC & EF are shadows]
5/DE = 12.5/20
DE = 5×20/12.5
DE = 8 feet
height of another tree = 8 feet
let the triangle be ABC and DEF
in triangle ABC and DEF
one angle is 90° in both triangles
& one angle is formed by the sun which is equal in both triangles because they form shadows at same time
therefore
Both triangles are similar by AA similarity
so there corresponding sides are proportional
AB/DE = BC/EF [AB and DE are heights of
[tree and BC & EF are shadows]
5/DE = 12.5/20
DE = 5×20/12.5
DE = 8 feet
height of another tree = 8 feet
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