Question

A 6-foot person standing 15 feet from a streetlight casts a 15-foot shadow. Two similar triangles are formed. One triangle is formed by the person and the shadow that the person casts. A second triangle is formed by the streetlight and the ground from the base of the streetlight to the end of the shadow.

The street light is __ times taller than the person

Answer 1

6/15=height of lamp/(15+15); 6/15=height of lamp/30; height of lamp=(30/15)6=2×6, 2 times taller.
(Lamp is 12 feet tall)

Answer 2

Answer: The street is 2 times taller than the person.

Explanation:

With reference to the figure

Let AB be the street light ,CE be the man of 6 foot height,CB be the distance between man and the street light and CD be the distance between shadow and the man.

Then in ΔCDE

`tan\theta=(CE)/(CD)=(6)/(15)=(2)/(5)\\\Rightrarrow\ tan\theta=(2)/(5)`

now, in ΔABD

`tan\theta=(AB)/(BD)=(AB)/(BC+CD)=(AB)/(15+15)=(AB)/(30)\\\Rightarrow\ AB=30*\ tan\theta=30*(2)/(5)=12cm`

∴ The height of street light is AB=12 cm=2×6cm

Hence,the street is 2 times taller than the person.