Question

Noah is 1.35 meters tall. At 10 a.m., he measures the length of a tree's shadow to be 31.55 meters. He stands 26.2 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 set up a proportion using the measurements given. The height of the tree is approximately 1.12 meters.

Step-by-step explanation:

To find the height of the tree, we can set up a proportion using the measurements given. Let's call the height of the tree 'x'. We know that Noah's height and the length of his shadow are proportional to the height of the tree and the length of the tree's shadow. So, we can write the proportion as:

1.35/31.55 = x/26.2

To solve for 'x', we can cross multiply:

1.35 * 26.2 = 31.55 * x

35.37 = 31.55 * x

Dividing both sides by 31.55, we get:

x = 35.37/31.55

x ≈ 1.12 meters

Answer 2

3.64 meters

Step-by-step explanation:

To find the height of the tree to the nearest hundredth of a meter, you can use the principle of similar triangles.

First, we can use the Pythagorean theorem to find the length of the hypotenuse of the right triangle formed by the height of the tree, the distance between the base of the tree and the point where the shadows meet, and the length of the shadow of the tree.

c = √(a² + b²)

c = √(h² + 26.2²)

Next, we can use the similar triangles to establish a ratio between the length of the shadow and the height of the tree and the length of the shadow and the distance from the tree.

shadow tree / height tree = shadow person / height person

31.55 / h = 31.55 / 26.2

Now, we can cross-multiply and divide to solve for h

h = 31.55 * 1.35 / 26.2

h = 3.64 meters

We can round it up to the nearest hundredth of a meter:

h = 3.64 meters

Therefore, the height of the tree is 3.64 meters to the nearest hundredth of a meter.