Question

The image of the tree on the film of a camera is of length 35 mm, The distance from the lens to the film 42mm, and the distance from the lens to the tree is 6m, How tall is the portion of the tree being photographed?

Answer 1

Hint: compare the ratio of horizontal to the vertical height and also apply the formula of similarities of the triangle. And then compare the sides without any mistakes and find the unknown quantity. Means indirectly we need to compare the \[{\text{tan\theta }}\]for the \[\Delta {\text{ABD}}\]and \[{\text{\Delta BCE}}\]. Which can be given as \[\dfrac{{BC}}{{AB}} = \dfrac{{AD}}{{CE}}\]. So here as the three terms are known we can easily calculate the one unknown terms by putting in the equation above.

Complete step by step Answer:
Let us draw a figure according to the given conditions

As the angle of inclination of both image and lens will be the same from point B and hence the ratio of base length and height will be equal
\[\dfrac{{BC}}{{AB}} = \dfrac{{AD}}{{CE}}\]
BC = be the base length from lens to the image of 42 mm
AB= be the base length from lens to the tree of 6m
CE = be the height of the image of 35 mm
AD = be the height of the object
As putting the values of known three terms we can calculate one unknown term as calculated below,
\[\dfrac{{42}}{{35}} = \dfrac{6}{{AD}}\]
And hence on calculating the above equation we can conclude that
\[b = 5m\]
Hence, the length of the object is 5m.

Note: Similar Triangles: Two triangles are said to be similar if their corresponding angles are equal and the corresponding sides are in proportion, in simple words they are of the same shape but different size.
Whereas congruent triangles have the same shape and size, in short, they are exactly the same.