Question

Marlo, who is standing near a tree during the day, measures her shadow to be 19 inches long. A nearby trees shadows is 66.5 inches long. If Marlo is 5.1 feet tall, how tall is the tree, in feet?

Answer 1

To find the height of the tree, we convert Marlo's height to inches, set up a similar triangles proportion with the heights and shadows, and solve for the tree's height before converting it back to feet.

Step-by-step explanation:

The student is asking how to calculate the height of a tree given the length of that tree's shadow and comparing it to a person's height and shadow length. This type of problem can be solved using similar triangles because the person and the tree create proportional triangles with their shadows.

First, we need to convert Marlo's height from feet to inches because shadow lengths are provided in inches:

• Marlo's height = 5.1 feet * 12 inches/foot = 61.2 inches

Now, we can set up a proportion because the triangles are similar:

• Marlo's height / Marlo's shadow length = Tree's height / Tree's shadow length

Substituting the known values into this proportion gives us:

• 61.2 inches / 19 inches = Tree's height / 66.5 inches

By cross-multiplying and solving for the Tree's height, we get:

• Tree's height = (61.2 inches * 66.5 inches) / 19 inches

After calculating, the Tree's height in inches must be converted back into feet:

• Tree's height in feet = Tree's height in inches / 12 inches/foot

After performing these calculations, we can determine the height of the tree in feet.