A tree casts a shadow 38 m long. At the same time, the shadow cast by a 34 centimeter tall statue is 69 cm long. Find the height of the tree to the nearest tenth.
h/38 = 0.34/0.69
To find the height of the tree, we can use the concept of similar triangles.
First, let's convert the length of the statue's shadow from centimeters to meters. Since 1 meter is equal to 100 centimeters, we have:
69 cm = 0.69 m
Now we can set up a proportion to solve for the height of the tree. The corresponding sides of the similar triangles are the height of the tree and the height of the statue, as well as their respective shadows.
Using the given values, we have:
(height of tree) / (length of tree's shadow) = (height of statue) / (length of statue's shadow)
Let's call the height of the tree H. Plugging in the values we know:
H / 38 m = 34 cm / 0.69 m
Now we can solve for H by cross-multiplying and then dividing:
H = (34 cm / 0.69 m) * 38 m
H ≈ 187 cm
Therefore, the height of the tree is approximately 187 centimeters.