a tree casts a shadow 29m long. at the same time the shadow cast b a 61cm tall statue is 82cm long. find the height of the tree. round results to the nearest unit.
Let's change meters to centimeters. Set up a proportion, cross multiply, and solve for x.
x/2900 = 61/82
82x = 176,900
x = 2,127.32 cm
x = 21.57 = 22 meters
61/82 = h/29
so
h = 61 * 29 / 82
= 21.6 meters high
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=21.6 m
To find 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: one formed by the tree and its shadow, and the other formed by the statue and its shadow.
Using the properties of similar triangles, we can set up the following proportion:
(height of the tree) / (length of the tree's shadow) = (height of the statue) / (length of the statue's shadow)
Substituting the given values:
h / 29 = 61 / 82
To solve for "h," we can cross-multiply and then divide:
h * 82 = 29 * 61
h = (29 * 61) / 82
Now, let's calculate the value of "h":
h = (29 * 61) / 82
h ≈ 21.58
Rounding to the nearest unit, the height of the tree is approximately 22 meters.