A 12ft. pole casts a shadow of 16ft. What is the distance between the end of the shadow and the top of the pole?

A^2 + 12ft^2 = 16^2
A^2 + 144 = 256
A^2 + 0 = 256 - 144
A^2 = 112
A^2 = SQRT of 112 or 10.58ft.

I agree.

144 + 256 = 400

Square root of 400 is 20

My answer makes more sense than yours.

You need to subtract 144 from each side and not add it. So.. I still agree with your answer.

To find the distance between the end of the shadow and the top of the pole, you can use the concept of similar triangles.

In this case, the height of the pole (let's call it A) and the length of the shadow (which is 16ft) are the corresponding sides of two similar triangles.

The ratio of the corresponding sides of similar triangles is proportional. So, we can set up the following proportion:

A / 12ft = 16ft / 12ft

Cross-multiplying, we get:

A * 12ft = 16ft * 12ft

A * 12ft = 192ft

Dividing both sides by 12ft, we obtain:

A = 192ft / 12ft

A = 16ft

Therefore, the distance between the end of the shadow and the top of the pole is 16ft.