Question

Nicole is 1.55 meters tall. At 2 p.m., she measures the length of a tree's shadow to be 30.05 meters. She stands 25.6 meters away from the tree, so that the tip of her shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Answer 1

The height of the tree is approximately 12.77 meters.

Explanation

In this scenario, we can employ similar triangles to determine the height of the tree. At 2 p.m., Nicole casts a shadow that aligns with the tree's shadow. Given Nicole's height of 1.55 meters and the distance between her and the tree (25.6 meters), along with the length of her shadow (30.05 meters), we establish a ratio.

The ratio of Nicole's height to her shadow's length remains constant. Therefore, using this ratio, we can calculate the height of the tree. This can be represented as:

Nicole's height / Nicole's shadow length = Tree's height / Tree's shadow length

With Nicole's height (1.55 meters), her shadow length (30.05 meters), and the distance between her and the tree (25.6 meters), we can calculate the tree's height:

Tree's height = (Nicole's height / Nicole's shadow length) * Tree's shadow length

Tree's height = (1.55 / 30.05) * 25.6 ≈ 12.77 meters

Therefore, the height of the tree, to the nearest hundredth of a meter, is approximately 12.77 meters.

Answer 2

approximately 1.81 meters.

Explanation:

Let's call the height of the tree "h". We can set up a proportion based on the similar triangles formed by Nicole, her shadow, the tree, and the tree's shadow:

(height of Nicole) / (length of Nicole's shadow) = (height of tree) / (length of tree's shadow)

Substituting the given values, we get:

1.55 / 25.6 = h / 30.05

Simplifying and solving for h, we get:

h = (1.55 / 25.6) * 30.05

= 1.81181640625

Rounding to the nearest hundredth, we get:

h ≈ 1.81 meters

the height of the tree is approximately 1.81 meters.