A tree casts a shadow that measures 5 m. At the same time, a meter stick casts a shadow that is 0.4 m long. How tall is the tree?
We will solve the problem by proportions.
Let the height of the tree be x, then
x/5 = 1/0.4
Cross-multiply to get
x=5*1/0.4=12.5 m.
Thus the tree is 12.5 m. tall
To find the height of the tree, we can use the concept of similar triangles.
Let's assume the height of the tree is 'h' meters.
We know that the length of the tree's shadow is 5 m, and the length of the meter stick's shadow is 0.4 m.
Using the properties of similar triangles, we can set up the following proportion:
h / 5 = 1 / 0.4
To solve for 'h', we can cross-multiply:
0.4h = 5 * 1
0.4h = 5
Now, divide both sides of the equation by 0.4 to isolate 'h':
h = 5 / 0.4
h = 12.5
Therefore, the height of the tree is 12.5 meters.