a girl 160 cm tall stands 360 cm from a lamp post at nicht. her shadow from the light is 90 cm long. how long is the lamp post?

Question

I don't know how to solve this question.

Answer 1

Hi Ally,

 

You could solve this using similar triangles

 

The larger triangle is formed by the lamp post as one leg the shadow on the ground as another leg and the distance from the top of the lamp post to the end of the shadow as the other side.

 

the smaller triangle is formed by the girl and her shadow.

 

These two triangles are similar since they are both right triangles and they share a common angle at the end of the shadow.

 

You should try to draw a picture representing this.

 

In any case,  once you know the triangles are similar you not that corresponding sides are proportional  and you can set up a proportion with the info you know.

 

let x = height of lamp post

 

160/90 = x/450

 

450 is the length from the base of the lamp post to the end of the shadow (360+90)

 

cross multiple

 

90x = 72000

 

x =800cm

 

hope this helps