Sam is 180cm tall. He stands 60 cm in front of a tall plane mirror.How tall is Sam's image

Amy is 160 cm tall and stands 50 cm in front of a plane mirror. The image of Amy is:

answer is 60-apex

To determine Sam's image height in the plane mirror, we can use the concept of similar triangles.

Here's how you can calculate it step by step:

1. Draw a diagram to represent the situation. Draw a vertical line to represent Sam's height (180cm) and label it as "Sam". Then draw a horizontal line to represent the mirror and position Sam 60cm in front of it.

2. Create a triangle between Sam's head, the mirror, and the position of Sam's image in the mirror. This triangle is a right-angled triangle with the vertical line representing Sam's height as the hypotenuse.

3. Since the mirror creates a reflection that is an equal distance behind it, the distance between Sam and his image in the mirror is also 60cm.

4. Now we have two right-angled triangles that are similar: the larger triangle representing Sam's height and the smaller triangle representing Sam's image height.

5. Use the ratio of corresponding sides of similar triangles to find the height of Sam's image. In this case, since Sam's image is smaller than Sam himself, the ratio of Sam's image height to Sam's actual height is the same as the ratio of the distance between Sam and his image (60cm) to the distance between Sam and the mirror.

So, we can set up the following equation:
image height / Sam's height = distance to image / distance to mirror

Plugging in the given values, we get:
image height / 180cm = 60cm / 60cm

Simplifying the equation:
image height / 180cm = 1

Rearranging the equation, we find that:
image height = 180cm

Therefore, Sam's image height in the mirror is 180cm, which is the same as his actual height.

The answer is 180