a tree is 10 ft. 3 in. tall. To find the height of a tower,the shadow of the tree and the shadow of the tower were measured. What is the height of h of the tower?
What was the heights of the tree's and tower's shadow?
To find the height of the tower, we can use a proportion involving the heights of the tree and its shadow, as well as the height of the tower and its shadow.
Let's denote the height of the tree as T (given as 10 ft. 3 in.), the length of its shadow as S, the height of the tower as H (which we need to find), and the length of the tower's shadow as x (which is also unknown).
The proportion we can set up is:
T/S = H/x
Now, we can substitute the given values:
10 ft. 3 in./S = H/x
To make the calculations simpler, let's convert the height of the tree to inches. There are 12 inches in a foot, so 10 ft. = 120 inches. Therefore, the height of the tree is 120 inches + 3 inches = 123 inches.
Substituting this value:
123 in./S = H/x
Now, let's say the length of the tree's shadow is 15 ft. 6 in. To convert this to inches, we get: 15 ft. × 12 in./ft. = 180 inches, and 180 inches + 6 inches = 186 inches.
Substituting this value:
123 in./186 in. = H/x
We can simplify this proportion by dividing both sides by 3:
41 in./62 in. = H/x
To find the height of the tower (H), we need to know the length of its shadow (x). If you provide the value of x, we can calculate H for you using this equation.