Jonathan is 3 ft from a lamppost that is 12 ft high. The lamppost and it's shadow form the legs of a right triangle. Jonathan is 6 ft tall and Is standing parallel to the lamppost. How long is Jonathan's shadow?
square root of 180
To find the length of Jonathan's shadow, we can use the concept of similar triangles.
Let's label the length of Jonathan's shadow as x.
In the given scenario, the lamppost creates a right triangle with its shadow, while Jonathan creates a similar right triangle with his shadow. Since the triangles are similar, we can set up a proportion using the corresponding sides:
Height of lamppost / Length of lamppost's shadow = Height of Jonathan / Length of Jonathan's shadow
Plugging in the values we know:
12 ft / x = 6 ft / 3 ft
To solve for x, cross-multiply and then simplify:
12 ft * 3 ft = 6 ft * x
36 ft = 6 ft * x
Now, we can solve for x by dividing both sides by 6 ft:
36 ft / 6 ft = x
x = 6 ft
Therefore, Jonathan's shadow is 6 ft long.