A 12ft tall building casts a shadow. The distance from the top of the building to the tip of the shadow is 18 ft
. Find the length of the shadow.
This sounds like a job for Pythagoras.
12^2 + b^2 = 18^2
144 + b^2 = 324
b^2 = 180
b = 13.4
To find the length of the shadow, you can set up a proportion using the height of the building and the length of the shadow. Let's call the length of the shadow "x".
We can set up the following proportion:
(Building Height)/(Shadow Length) = (Height from Top to Shadow)/x
Substituting the given values:
12 ft / x = 18 ft / (12 + x)
Next, we can cross-multiply:
12(12 + x) = 18x
144 + 12x = 18x
Now, let's isolate "x" on one side:
18x - 12x = 144
6x = 144
Divide both sides by 6:
x = 144/6
x = 24
Therefore, the length of the shadow is 24 ft.
To find the length of the shadow, you can set up a proportion using the given information.
Let's label the height of the building as "h" and the length of the shadow as "s". According to the problem, the height of the building (h) is 12 feet and the distance from the top of the building to the tip of the shadow is 18 feet.
Using a proportion, we can set up the equation:
h / s = (distance from top of building to tip of shadow) / (length of the shadow)
Substituting the given values:
12 / s = 18 / s
Now, we can solve for s by cross-multiplying:
12s = 18 * s
Dividing both sides of the equation by 12, we get:
s = 18 * s / 12
Simplifying, we have:
s = 1.5 * s
To solve for s, we can divide both sides of the equation by s:
1 = 1.5
This equation is not possible, as 1 is not equal to 1.5.
Therefore, we cannot determine the length of the shadow based on the given information.