In a garden, a birdbath 2ft 6 in. tall casts an 18-in. shadow at the same time an oak tree casts a 90-ft shadow. How tall is the oak tree?
Cross multiply and solve for x.
2.5/1.5 = 90/x
wrong
To find the height of the oak tree, we can use the concept of similar triangles. Let's label the height of the oak tree as "h" and its shadow as "s". Similarly, let's label the height of the birdbath as "b" and its shadow as "t".
We are given that the height of the birdbath is 2 feet 6 inches, which is equivalent to 30 inches. The shadow of the birdbath is 18 inches.
We are also given that the shadow of the oak tree is 90 feet.
Now, using the concept of similar triangles, we can set up the following proportion:
(birdbath height) / (birdbath shadow) = (oak tree height) / (oak tree shadow)
Plugging in the values we know:
30 inches / 18 inches = h / 90 feet
To solve for "h", we need to convert the units to be consistent. Since we are working with feet for the oak tree shadow, let's convert the birdbath height and shadow to feet:
30 inches = 2.5 feet
18 inches = 1.5 feet
Now we can solve the proportion:
2.5 feet / 1.5 feet = h / 90 feet
Cross-multiplying:
1.5h = 2.5 * 90
Multiply:
1.5h = 225
Divide both sides by 1.5:
h = 225 / 1.5
Calculating:
h = 150 feet
Therefore, the oak tree is 150 feet tall.