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 = (p)/(b) = (height)/(shadow) = (x )/(7)`

height of man = 1.6m

length of man shadow= 4m

For man :-

`\tan\theta = (p)/(b) = (height)/(shadow) = (1.6)/(4)`

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

So according to questions :-

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

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