A tree casts a shadow 36 m long. At the same time, the shadow cast by a 49-centimeter tall statue is 90 cm long. Find the height of the tree. Round to the nearest tenth.
Change meters to cm.
49/90 = x/3600
Solve for x.
To find the height of the tree, we can set up a proportion between the height of the tree and the length of its shadow, and the height of the statue and the length of its shadow.
Let's denote:
- Height of the tree as T
- Length of the tree's shadow as S
- Height of the statue as H
- Length of the statue's shadow as S'
We can write the proportion as:
T/S = H/S'
We are given that the length of the tree's shadow (S) is 36 m and the length of the statue's shadow (S') is 90 cm.
Since the units must match, let's convert the length of the statue's shadow to meters:
90 cm = 90/100 m = 0.9 m
Now we can substitute the known values into the proportion:
T/36 = 49/0.9
To solve for T, we cross multiply:
T = (36 * 49) / 0.9
T = 1,964 / 0.9
T ≈ 2182.2
Therefore, the height of the tree is approximately 2182.2 meters. Rounded to the nearest tenth, the height of the tree is 2182.2 meters.