A boy is standing 25 ft away from a street light that is 20 ft tall.How tall is he if his shadow is 5 ft long?
nuts
To find the height of the boy, we can use similar triangles. Let's consider two triangles: the triangle formed by the boy, his shadow, and the street light, and the triangle formed by the boy, his height, and his shadow.
In the first triangle, we have the height of the street light (20 ft), the distance from the street light to the boy (25 ft), and the length of the shadow (5 ft). Let's call the height of the boy "h."
Using the properties of similar triangles, we can set up the following proportion:
(height of the street light) / (distance from the street light to the boy) = (height of the boy) / (length of the shadow)
Plugging in the given values, we get:
20 / 25 = h / 5
Now, let's solve for h:
20 * 5 = 25 * h
100 = 25h
Dividing both sides by 25:
100 / 25 = h
4 = h
Therefore, the height of the boy is 4 ft.
h/5 = 20/(25+5)
h = 100/30 = 10/3 = 3.33 ft