Height and distance comparison.

Question

A man 6ft tall casts a shadow 4ft long. At the same time, a flag casts a shadow 50ft long. Find the height of the flag.

Answer 1

Hint: Use proportions,

$\frac{6}{4}=\frac{x}{50}\implies x=75$

Answer 2

You can also use similar triangles to get the answer as:$$\frac{6}{4} = \frac{x}{50} \Rightarrow x=75$$ where $x$ refers to the height of the shadow cast by the flag.

Answer 3

Let AC and DF be man and flag respectively. BC and EF are their shadows respectively.

At the same time light rays from the sun will fall on the man and flag at the same angle.

Therefore,

$\angle$CAB = $\angle$FDE

$\angle$CBA = $\angle$FED

Also,

$\angle$ACB = $\angle$DFE = 90 degree

By AAA property triangle ABC and DEF are similar.

$\frac{AC}{DF} = \frac{BC}{EF}$

$\frac64 = \frac{x}{50}$

$4x = 50 * 6$

$x = 75 ft$