Question

Please Help

the figure shows a child estimating the height of a tree by looking at the top of the tree with a mirror assuming that both the child and tree form right angles with the ground which of the following proportions can be used to estimate the height of the tree.

Answer 1

Option: C is the correct answer.

`(h)/(4)=(12)/(5)`

Explanation:

Clearly from the diagram shown we could see that the angle formed at the base is the same.

Let the angle be theta (θ).

Hence, in the small right angled triangle ΔACB we have:

`\tan \theta=(AC)/(CB)\\\\\tan \theta=(4)/(5)------(1)`

Similarly in the right angled triangle ΔEDB we have:

`\tan \theta=(ED)/(DB)\\\\\tan \theta=(h)/(12)------(2)`

Hence, on equating equation (1) and equation (2) we have:

`(4)/(5)=(h)/(12)\\\\(h)/(4)=(12)/(5)`

Hence, option:C is the correct option.