Question

The picture shows a person taking a pinhole photograph of himself. Light entering the opening reflects his image on the wall, forming similar triangles. What is the height of the image to the nearest inch?

Answer 1

Since the triangle formed is similar, then the ratio of the triangle height(horizontal distance) and the base of the triangle(the person and image height) will be same. The calculation would be:

a/b= c/d
16in / (4ft + 8in)= c/ (5ft + 3in)
16in/(48in + 8in)= c/ (60in + 3 in)
16in/64in= c/63in
c=1/4 * 63 in= 15.75 in= 16inch

Answer 2

Answer:

The height of the image is 18 inch.

Step-by-step explanation:

It is given that the light entering the opening reflects his image on the wall, forming similar triangles.

We know that

1 ft =12 inch

The height of person is

$5\text{ ft }3\text{ in}=5\times 12+3=63\text{ in}$

The distance of person form the wall is

$4\text{ ft }8\text{ in}=4\times 12+8=56\text{ in}$

The distance of image form the wall is 16 in.

Let the height of image be x.

The corresponding sides of similar triangles are proportional.

$\frac{x}{16}=\frac{63}{56}$

$x=\frac{63}{56}\times 16$

$x=18$

Therefore the height of the image is 18 inch.