At noon, Cesar cast a shadow 0.15 foot long. Next to him a streetlight cast a shadow 0.25 foot long. If Cesar is 6 feet tall, how tall is the streetlight?

2 Answers
EZ as pi
Jul 15, 2018

#10 # feet tall.

Explanation:

The two triangles formed by Cesar and his shadow and the streetlight and its shadow are similar triangles because the sun is shining at the same angle.

You can therefore compare the heights and the lengths of the shadows as a direct proportion.

#6/0.15 = x/0.25" "(larr "heights")/(larr "shadows")#

#x = (6xx0.25)/0.15#

#=10 # feet tall.

Harish Chandra Rajpoot
Jul 15, 2018

#10\ \text{feet}# tall

Explanation:

Let #\theta# be the angle of elevation of the sun at given instant of time then

#\tan\theta=\frac{\text{Height of Cesar}}{\text{Length of shadow of Cesar}}#

#\tan\theta=\frac{6}{0.15}#

#\tan\theta=40#

Similarly, for streetlight of height #H#, we have

#\tan\theta=\frac{\text{Height of streetlight}}{\text{Length of shadow of streetlight}}#

#40=\frac{H}{0.25}#

#H=0.25\cdot 40#

#H=10#

Hence, the height of streetlight is #10\ \text{feet}#

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