Question

A six foot man is standing 10 feet away from a 20 foot lamppost. what is the length of his shadow?

Answer 1

Answer:

4.29 feet ( approx )

Step-by-step explanation:

Let x be the length of the shadow of man,

Given,

The height of the man = 6 feet,

The height of the lamppost = 20 foot,

Distance of the man from the lampost = 10 feet,

By making the diagram,

We found two similar triangles in which first triangle having sides 6 and x,

Second triangle having sides 20 and x + 10,

∵ The corresponding sides of similar triangle are in same proportion,

$\implies \frac{x}{x+10}=\frac{6}{20}$

$20x = 6x + 60$

$20x - 6x = 60$

$14x = 60$

$\implies x = \frac{60}{14}=4.28571428571\approx 4.29$

Hence, the length of the shadow is approximately 4.29 feet.

Answer 2

There are two congruent triangles that are being formed from the lamppost, the light, the ground and the man. Always try to draw a picture for these types of problems. It helps a lot when solving. Your answer should be about 4.3ft