Question

Kate stands 2 meters from a lamppost. She is 2.1 meters tall and casts a shadow 3 meters long in the light from the lamp. How tall is the lamppost? See diagram below.​

Answer 1

3.5 meters.

Explanation:

Please refer to the attachment.

Since the two triangles share two congruent angles, by AA Similarity, the two triangles are similar.

Therefore, we can write the following proportion:

`(3)/(5)=(2.1)/(x)`

To find the height of the lamppost x, we will simply have to solve for x.

So, let’s cross-multiply:

`10.5=3x`

Divide both sides by 3:

`x=10.5/3=3.5`

Hence, the height of the lamppost is 3.5 meters.