Question

A 6-foot hiker casts a 9-foot shadow, and a nearby tree casts a 31-foot shadow. To the nearest tenth, the height of the tree is blank feet.

Answer 1

Using proportions based on similar triangles, the height of the tree, to the nearest tenth, is found to be 20.7 feet.

Step-by-step explanation:

To find the height of the tree, we can use the shadow lengths and the hiker's height to set up a proportion because the sun's rays provide similar triangles. Let x be the height of the tree. We know that the hiker is 6 feet tall and casts a 9-foot shadow, so the ratio of the hiker's height to his shadow is 6/9. We can set this proportional to the tree's height and its shadow:

• 6 feet (hiker's height) / 9 feet (hiker's shadow) = x feet (tree's height) / 31 feet (tree's shadow)

By cross-multiplying to solve for x, we get:

6/9 = x/31

9x = 6 * 31

x = (6 * 31) / 9

x = 20.666666...

To the nearest tenth, the height of the tree is 20.7 feet.