4. Tonya is 1.3 meters tall. She stands 7 meters in front of a tree and casts a shadow 1.8 meters long. How tall is the tree?
6.35555 Meters tall?
1.3/1.8 = h/(7+1.8)
The tree is 6 whole meters long with a little extra .
To determine the height of the tree, we can use the concept of similar triangles. Let's denote the height of the tree as "h."
We have two similar triangles: Tonya's shadow triangle and the tree triangle. The corresponding sides of these triangles are proportional, according to the properties of similar triangles.
In Tonya's shadow triangle, we have the following measurements:
- Height of Tonya (opposite side) = 1.3 meters
- Length of the shadow (adjacent side) = 1.8 meters
In the tree triangle, we need to find:
- Height of the tree (opposite side) = h
- Length of the tree's shadow (adjacent side) = ?
We can set up a proportion using the corresponding sides of the triangles:
Tonya's height / Tonya's shadow length = Tree's height / Tree's shadow length
Substituting the given values:
1.3 meters / 1.8 meters = h / Tree's shadow length
To find the length of the tree's shadow, we can use the fact that Tonya is 7 meters in front of the tree. Therefore, the tree's shadow length is 7 meters.
Now we can solve for h:
1.3 meters / 1.8 meters = h / 7 meters
Cross-multiplying:
1.3 meters * 7 meters = 1.8 meters * h
9.1 = 1.8h
Dividing both sides by 1.8:
9.1 / 1.8 = h
h ≈ 5.0556 meters
Therefore, the height of the tree is approximately 5.0556 meters.