contestada

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

Respuesta :

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)
JeanaShupp

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

Step-by-step 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

[tex]tan\theta=\frac{CE}{CD}=\frac{6}{15}=\frac{2}{5}\\\Rightrarrow\ tan\theta=\frac{2}{5}[/tex]

now, in ΔABD

[tex]tan\theta=\frac{AB}{BD}=\frac{AB}{BC+CD}=\frac{AB}{15+15}=\frac{AB}{30}\\\Rightarrow\ AB=30\times\ tan\theta=30\times\frac{2}{5}=12cm[/tex]

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

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


Ver imagen JeanaShupp

Otras preguntas