At 4 pm, Jack who is 6 ft tall cast a shadow that is 4 1/2 ft long. At the same time, a nearby free cast a shadow that is 12 ft long, how tall is the tree?
Well, it seems Jack's shadow is running a bit behind, while the tree's shadow is stretching out like Usain Bolt on a sunny day. To solve this height crisis, we can set up a ratio!
If Jack, who is 6 ft tall, casts a 4 1/2 ft shadow, we can say that his height is to his shadow as the tree's height is to its shadow.
Let's call the tree's height 'T'. So we have:
6 ft / 4.5 ft = T ft / 12 ft
Now let's do some math magic!
(6 / 4.5) x 12 = T
8 ft = T
So, according to my hilarious calculations, the tree is 8 ft tall! Now remember, that's assuming the tree isn't wearing platform shoes or moonlighting as a giraffe.
To find out how tall the tree is, we can use the concept of similar triangles. Similar triangles have proportional sides.
Let's denote the height of the tree as 'h'.
We have two similar triangles: one formed by Jack's height and his shadow, and the other formed by the height of the tree and its shadow.
The first triangle is formed by Jack's height (6 ft) and his shadow (4 1/2 ft). The second triangle is formed by the height of the tree (h) and its shadow (12 ft).
We can set up a proportion:
Jack's height / Jack's shadow = Tree's height / Tree's shadow
6 ft / 4 1/2 ft = h / 12 ft
To simplify the fractions, we can change 4 1/2 ft to an improper fraction:
6 ft / (9/2) ft = h / 12 ft
Next, we can simplify the equation by multiplying the denominators and numerators:
6 ft * (2/9 ft) = h * (1/12 ft)
12/9 ft = h/12 ft
Cross-multiplying:
(12/9) * 12 ft = h * 1 ft
Simplifying the equation further:
h = (12/9) * 12 ft
Now we can calculate the value of h:
h = 16 ft
Therefore, the tree is 16 ft tall.
The ratio of heights is the same as the ratio of shadow lengths.
x/6 = 12/4.5