Question

At a given time of day, the ratio of the height of an object to the length of its shadow is the same for all objects. If a 2-ft stick in the ground casts a shadow of 0.4 ft, find the height of a tree that casts a shadow that is 7.64 ft.

a. 3.82 ft
b. 38.2 ft
c. 7.28 ft
d. 72.8 ft

Answer 1

To find the height of the tree, we use the ratio of height to shadow length from a 2-ft stick (which is 5) and apply it to the tree's shadow of 7.64 ft to find that the height of the tree is 38.2 ft (option b).

Step-by-step explanation:

The question asks us to find the height of a tree based on the shadow it casts and using the ratio of the height to the shadow length from a smaller object.

The ratio for the 2-ft stick and its shadow (0.4 ft) is as follows:

1. Height of stick: 2 ft
2. Shadow of stick: 0.4 ft
3. Ratio (Height to Shadow): 2 ft / 0.4 ft = 5

This ratio is the same for all objects, including the tree. Now, using the shadow of the tree (7.64 ft):

1. Shadow of tree: 7.64 ft
2. Height of tree: x (unknown)
3. Ratio (Height to Shadow for tree): x / 7.64 ft = 5

To find the tree's height, we solve for x:

1. x = 5 × 7.64 ft
2. x = 38.2 ft

Therefore, the height of the tree is 38.2 ft, which corresponds to option b.