Question

A traffic sign casts a shadow 7m long at the same time a person 1.6m tall casts a shadow 4m long. Find the height of the sign.​

Answer 1

height of sign = x

length of sign shadow = 7m

For sign:-

$tan \theta = \frac{p}{b} = \frac{height}{shadow} = \frac{x }{7}$

height of man = 1.6m

length of man shadow= 4m

For man :-

$\tan\theta = \frac{p}{b} = \frac{height}{shadow} = \frac{1.6}{4}$

tanθ is same bez sun is at same level (angle) for both of them

So according to questions :-

$\tan( \theta) = \frac{x}{7} = \frac{1.6}{4} \\ \frac{x}{7} = \frac{ \cancel{1.6}^{ \: \: 0.4} }{ \cancel4} \\ x = 7 \times 0.4 \\ x = 2.8m \:$

so we can say height of the sign = x = 2.8 m