At a point 16 yards from the base of a tower,the distance to the top of the tower is 4 ysrds more than the height of the tower.Find the height of the tower.

looks like a regular Pythagorean problem

Height of tower --- x
hypotenuse ---- x+4
base ----- 16
x^2 + 16^2 = (x+4)^2
x^2 = 256 = x^2 + 8x + 16
240 = 8x
x = 30

To find the height of the tower, we can use the Pythagorean theorem. According to the problem, we know that the distance from the base of the tower to the top (the hypotenuse) is 4 yards more than the height of the tower (one of the legs). We can set up the equation as follows:

Let x be the height of the tower.

Using the Pythagorean theorem, we have:

x^2 + 16^2 = (x + 4)^2

Simplifying this equation, we get:

x^2 + 256 = x^2 + 8x + 16

Subtracting x^2 from both sides, we have:

256 = 8x + 16

Subtracting 16 from both sides, we get:

240 = 8x

Dividing both sides by 8, we find:

x = 30

Therefore, the height of the tower is 30 yards.