Question

A flagpole casts a shadow that is 50 feet long. At the same time, a woman standing nearby who is 6 feet tall casts a shadow that is 3 ft long. How tall is the flagpole?

Answer 1

The height of the flagpole is 100 feet.

What are shadows?

Shadows are area devoid of light as a result of the obstruction of light by an opaque object.

Analysis:

The length of the shadow and the height of the flagpole are at right angles.

Similarly, the height of the woman and the length of her shadow are at right angles. Making both similar right-angled triangles.

The ratio of the height of the woman to that of pole is equal to ratio of the length of woman's shadow to that of the flagpole.

let length of flagpole be h.

height of woman = 6 feet

length of shadow of woman = 3 feet

length of shadow of pole = 50 feet.

$\frac{6}{h}$ = $\frac{3}{50}$

3h = 300

h = 100 feet

In conclusion, the height of the flag pole is 100 feet.

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