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At a given time of​ day, the ratio of the height of an object to the length of its shadow is the same for all objects. If a 4​-ft stick in the ground casts a shadow of 2.8 ​ft, find the height of a tree that casts a shadow that is 24.64 ft.

Respuesta :

Answer:35.2 ft

Explanation:

Given

height of stick =4 ft

shadow length =2.8 ft

Angle of elevation of sun is

[tex]tan\theta =\frac{4}{2.8}[/tex]

let the height of tree be h

as [tex]\theta [/tex]will remain same thus

[tex]tan\theta =\frac{h}{24.64}[/tex]

[tex]\frac{4}{2.8}=\frac{h}{24.64}[/tex]

h=35.2 ft