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?
2.5/1.5 = x/90
Cross multiply and solve for x.
1.5x = 225
x = 150 feet
To find the height of the oak tree, we can set up a proportion using the shadow lengths of the birdbath and the oak tree.
Let's first convert the height of the birdbath to inches. Since 1 ft equals 12 inches, the height of the birdbath is (2 x 12) + 6 = 30 inches.
We can set up the proportion as follows:
Height of birdbath / Shadow length of birdbath = Height of oak tree / Shadow length of oak tree
Plugging in the values we know, we have:
30 inches / 18 inches = Height of oak tree / 90 feet
To solve for the height of the oak tree, we can cross-multiply and solve for the unknown:
(30 inches x 90 feet) = (18 inches x Height of oak tree)
2700 inches * feet = 18 inches * Height of oak tree
Dividing both sides by 18 inches gives us:
Height of oak tree = (2700 inches * feet) / 18 inches
Simplifying, we get:
Height of oak tree = 150 feet
Therefore, the oak tree is 150 feet tall.
To find the height of the oak tree, we can use a proportion based on the information given. Let's set up the proportion:
Height of birdbath / Shadow of birdbath = Height of oak tree / Shadow of oak tree
We know that the birdbath is 2ft 6in tall, which can be converted to 2.5ft. The shadow of the birdbath is given as 18 inches.
Now, we need to convert the shadow of the oak tree into the same unit of measurement as the birdbath. The shadow of the oak tree is given as 90ft.
Since both shadows are in feet, we can directly use the given values to set up the proportion:
2.5ft / 18in = Height of oak tree / 90ft
To simplify the proportion, we need to convert 18 inches to feet by dividing it by 12, since there are 12 inches in a foot:
2.5ft / (18in / 12) = Height of oak tree / 90ft
Now, calculate the right side of the proportion:
2.5ft / 1.5ft = Height of oak tree / 90ft
Next, we can cross-multiply the proportions:
(2.5ft * 90ft) / 1.5ft = Height of oak tree
Simplifying:
225ft² / 1.5ft = Height of oak tree
We can now solve for the height of the oak tree:
Height of oak tree = 225ft² / 1.5ft
Height of oak tree = 150ft
Therefore, the oak tree is 150 feet tall.