176,796 views
32 votes
32 votes
Anand is 1.75 meters tall. At 10 a.m., he measures the length of a tree's shadow to be

41.35 meters. He stands 36.9 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.

User David Wolf
by
2.6k points

2 Answers

6 votes
6 votes

Final answer:

To find the height of the tree, use similar triangles and proportions. Set up a proportion between Anand's height and the length of his shadow, and solve for the height of the tree which is 24.45 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 the height of the tree as 'h'.

From the given information, we know that Anand's height is 1.75 meters and the length of his shadow is 41.35 meters. Anand stands 36.9 meters away from the tree.

Using the concept of similar triangles, we can set up the following proportion:

1.75 / 41.35 = (1.75 + h) / h

Cross multiplying and solving for 'h', we get:

h = (1.75 * h) / 41.35 + 1.75

Now, substitute the value of h into the equation and solve for h:

h = (1.75 * (36.9 + h)) / 41.35 + 1.75

Simplifying the equation will give you the height of the tree, which is approximately 24.45 meters.

User Mseancole
by
2.7k points
13 votes
13 votes

Answer:

16.26

Step-by-step explanation:

trust

User Mups
by
2.4k points
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