Question

Mamadou is 1.35 meters tall. At 3 p.m., he measures the length of a tree's shadow to be 34.05 meters. He stands 29.1 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter.

Answer 1

To find the height of the tree, we can use similar triangles and proportions. Setting up equations using the ratios of Mamadou's height to the height of the tree and their respective distances to the tree, we can solve for the unknowns. Using the given measurements, the height of the tree is approximately 27.75 meters.

Step-by-step explanation:

To find the height of the tree, we can use similar triangles and the concept of proportions. Let's denote Mamadou's height as h and the height of the tree as t. From the given information, we have the following ratio:

h / 1.35 = t / 34.05

Solving for t (height of the tree):

t = 34.05 * h / 1.35 = 25 * h

Since Mamadou stands 29.1 meters away from the tree, we can also set up a proportion using the lengths of the shadows:

h / 1.35 = t / (34.05 - 29.1)

Substituting t = 25 * h:

h / 1.35 = (25 * h) / (34.05 - 29.1)

Solving for h (Mamadou's height):

h = (25 * 1.35) / (34.05 - 29.1)

Calculating this expression gives us the height of Mamadou, which is approximately 1.11 meters. Therefore, the height of the tree is approximately 25 * 1.11 = 27.75 meters.