1.Find the height to the nearest foot of a tree that makes a 50-foot shadow when a 2 ft. 6 in. pole is used to make a shadow of 3 feet.
please show your work
3 - x > 7. Subtract 3 from both sides: -x > 4. Multiply both sides by -1: x 7 + x, then subtract 7 from both sides: -4 > x, which means the same as x < -4
To find the height of the tree, we can set up a proportion between the height of the tree, the length of its shadow, and the length of the pole's shadow.
Let x be the height of the tree.
The proportion can be set up as:
x / 50 = (2 + 6/12) / 3
First, let's convert 2 ft 6 in to feet:
2 ft + 6/12 ft = 2.5 ft
Now we can rearrange the proportion and solve for x:
x = (50 * 2.5) / 3
x = 125 / 3
Using long division, we can find the decimal approximation of the height:
125 ÷ 3 = 41.67
To the nearest foot, the height of the tree is 42 feet.
To find the height of the tree, we can use a proportion. Let's call the height of the tree 'h'.
We have the following information:
- The height of the pole is 2 feet and 6 inches, which can be converted to 2.5 feet (since there are 12 inches in a foot).
- The length of the shadow cast by the pole is 3 feet.
- The length of the shadow cast by the tree is 50 feet.
We can set up a proportion using the ratios of the height of the pole to its shadow and the height of the tree to its shadow:
(2.5 feet / 3 feet) = (h / 50 feet)
Now, we can solve this proportion to find the height of the tree.
To do this, we can cross-multiply:
2.5 * 50 = 3 * h
125 = 3h
Dividing both sides of the equation by 3:
h = 125 / 3
The height of the tree is approximately 41.67 feet.
Therefore, the height of the tree, to the nearest foot, is 42 feet.
The 2.5 ft tree makes a 3ft shadow. That means the shadow is 1.2 times the height.
So, 1.2 * 50 = 60, and the tree's shadow is 60 ft.
Or, algebraically,
s/50 = 3/2.5
2.5s = 150
s=60