A 6 ft tall person cast a shadow 15 ft long. At the same time a nearby tower casts a shadow 100 ft long. Find the height of the tower.
the person is 2/5 as big as the shadow.
So, what's 2/5 * 100?
To find the height of the tower, we can use the concept of similar triangles. The height of the person and the height of the tower are proportional to the lengths of their respective shadows.
Let's assign variables to the unknowns:
- Height of the person = a
- Shadow of the person = x
- Height of the tower = b
- Shadow of the tower = y
We know that the person is 6 ft tall and their shadow is 15 ft long, so we have the first set of ratios:
a / x = 6 / 15
We can simplify this ratio by dividing both sides by the greatest common divisor, which is 3:
(a / 3) / (x / 3) = 6 / 15
a / (x / 3) = 2 / 5
Similarly, we know that the shadow of the tower is 100 ft long, so we have:
b / y = a / x
Now we can substitute the ratio a / x from the first equation into the second equation:
b / y = (2 / 5)
To find the height of the tower, we need to isolate b. We can rewrite the equation as:
b = (2 / 5) * y
Now we can substitute the value of y, which is 100 ft:
b = (2 / 5) * 100
b = 40 ft
Therefore, the height of the tower is 40 ft.