A man is 6ft tall is standing 10 feet from the base of a lamp post. The mans shadow has a lenght of 4ft . How tal is he lamp post

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To find the height of the lamp post, we can use similar triangles.

Let's represent the height of the lamp post as "h". The man's height is given as 6ft, and his shadow length is 4ft.

We have two similar triangles: the man's triangle and the lamp post's triangle. The corresponding sides of these triangles are in proportion.

The corresponding sides are:
Man's height = 6ft
Man's shadow length = 4ft
Lamp post's height = h (what we want to find)
Lamp post's shadow length = 10ft

Using the proportion of corresponding sides, we can set up an equation:

Man's height / Man's shadow length = Lamp post's height / Lamp post's shadow length

6ft / 4ft = h / 10ft

Simplifying the equation, we get:

6 / 4 = h / 10

Now, we can cross multiply:

6 * 10 = 4 * h

60 = 4h

Divide both sides by 4:

h = 60 / 4

h = 15

Therefore, the height of the lamp post is 15 feet.

To find the height of the lamp post, we can use similar triangles.

Let's represent the height of the lamp post as 'x'.

According to the problem, the man's height is 6ft, and the length of his shadow is 4ft.

We can set up a ratio based on the similar triangles formed by the man, his shadow, and the lamp post:

Height of the man / Length of the man's shadow = Height of the lamp post / Distance of the man from the lamp post

Plugging in the given values, we get:

6ft / 4ft = x / 10ft

Cross-multiplying, we have:

6ft * 10ft = 4ft * x

60ft = 4ft * x

Dividing both sides by 4ft:

60ft / 4ft = x

15ft = x

Therefore, the height of the lamp post is 15ft.