Question

Hank can see the top of a tree in a mirror that is placed 475 cm from the tree when he stands 190 cm from the mirror. What is the height of the tree?

Answer 1

The height of the tree is 430cm

Explanation:

Given

The attached illustration

Required

The height of the tree

Let:

`h \to` Hank's height

`H \to` Tree height

`d \to` distance between Hank and Mirror

`D \to` distance between tree and Mirror

From the question, we have:

`\angle 1 = \angle 2`

This means that:

`(H)/(D) = (h)/(d)`

Make H the subject

`H = (h)/(d) * D`

So, we have:

`H = (172cm)/(190cm) * 475cm`

`H = (172* 475cm)/(190)`

`H = (81700cm)/(190)`

`H = 430 cm`