A pine tree casts a shadow that is 49 feet long. A 10 foot sign next to it casts a shadow that is 8 feet long. How tall is the pine tree?
cross multiply
x/49 = 10/8
solve for x
61.25
To find the height of the pine tree, we can use the concept of similar triangles.
Let's label the height of the pine tree as "h" and its shadow as "s". Similarly, we can label the height of the sign as "10" and its shadow as "8".
Using the properties of similar triangles, we can set up the following proportion:
h/s = 10/8
Now, we can substitute the given values into the proportion:
h/49 = 10/8
To solve for "h," we can cross-multiply:
8h = 10 * 49
8h = 490
Next, divide both sides of the equation by 8:
h = 490/8
Simplifying the right side gives:
h = 61.25
Therefore, the pine tree is approximately 61.25 feet tall.