A tower casts a shadow of 64 feet. A 6 foot tall pole near the tower casts a shadow 8 feet long. How tall is the tower?

Cross multiply and solve for x

6/8 = x/68

48

To find the height of the tower, we can use the property of similar triangles. In this case, the ratio of the height of the tower to the height of the pole must be equal to the ratio of their respective shadows.

The height of the pole is given as 6 feet, and its shadow is 8 feet long. Let's call the height of the tower x feet and its shadow y feet.

So, we have the proportion:
6 feet / 8 feet = x feet / y feet.

To solve for x, we can cross multiply:
6 feet * y feet = 8 feet * x feet.

This simplifies to:
6y = 8x.

Now, let's use the additional information given that the tower's shadow is 64 feet long. This gives us another proportion:
6 feet / 8 feet = x feet / 64 feet.

Again we can cross multiply:
6 feet * 64 feet = 8 feet * x feet.

This simplifies to:
384 = 8x.

Now we have a system of equations:
6y = 8x,
384 = 8x.

We can solve this system by substitution or elimination.

Let's use elimination to solve for x by multiplying the first equation by 8 and subtracting it from the second equation:
384 - (8 * 6y) = 8x - 8x,
384 - 48y = 0.

Simplifying the equation gives us:
-48y = -384,
y = 8.

Now we can substitute the value of y back into the first equation to solve for x:
6(8) = 8x,
48 = 8x,
x = 6.

Therefore, the height of the tower is 64 feet.