Each time Old Faithful in Yellowstone National Park erupts, rangers can estimate the height of the geyser by comparing it to the height of a tree. First the rangers locate a tree of the same height. The shadow of the tree is 93 ft at the same time that the shadow of a 6 ft ranger is 4 ft. Find the height of the tree to the nearest foot.
my question is: how do they find a tree of the same height? There are none growing nearby.
Anyway, using similar triangles, the height h can be found using
h/93 = 6/4
To find the height of the tree, we can set up a proportion using the information given. Let's call the height of the tree "x".
We know that the tree's shadow is 93 ft when the shadow of a 6 ft ranger is 4 ft.
Using this information, we can set up the following proportion:
(tree height) / (tree shadow) = (ranger height) / (ranger shadow)
x / 93 = 6 / 4
To solve for x, we can cross-multiply:
4x = 6 * 93
4x = 558
Now we divide both sides by 4 to isolate x:
x = 558 / 4
x = 139.5
Therefore, the height of the tree is 139.5 ft to the nearest foot.