A man is walking away from a lamppost with a light source h = 6 m above the ground. The man is m = 1.5 m tall. How long is the man's shadow when he is d = 12 m from the lamppost? [Hint: Use similar triangles.]
(s+12)/6 = s/1.5
s=4
To find the length of the man's shadow, we can use similar triangles. Let's denote the length of the man's shadow as s.
First, we need to visualize the situation. We have a lamppost with a light source above the ground, and a man walking away from the lamppost. The man's height is 1.5 m and the light source is 6 m above the ground.
Since the light coming from the lamppost will form similar triangles with the man and his shadow, we can set up the following proportion:
height of man / length of man's shadow = height of lamppost / distance from lamppost to man
We know the height of the man (1.5 m), the height of the lamppost (6 m), and the distance from the lamppost to the man (12 m). We can substitute these values into the proportion:
1.5 / s = 6 / 12
Now we can simplify and solve for the length of the man's shadow, s:
1.5 / s = 6 / 12
To simplify the equation, we can cross-multiply:
1.5 * 12 = 6 * s
18 = 6s
Finally, we can solve for s by dividing both sides of the equation by 6:
18 / 6 = s
3 = s
Therefore, the length of the man's shadow is 3 meters when he is 12 meters away from the lamppost.