A tower casts a shadow 11 feet long. The distance from the top of the tower to the end of the shadow is 61 feet. how many feet tall is the tower?

61Squared = 11squared = h squared
3721 = 121 + h squared
-121 = -121
3600 = h squared
I get stuck at this point. Please help!

I think you then have to take the square root of 3600 to solve for just h and you would get 60ft.

I just need help I don't even know where to begin

To find the height of the tower, we can use the Pythagorean theorem, which states that the square of the hypotenuse (the distance from the top of the tower to the end of the shadow) is equal to the sum of the squares of the other two sides (the height of the tower and the length of the shadow).

Let's use the following variables:
h = height of the tower
s = length of the shadow (11 feet)
d = distance from the top of the tower to the end of the shadow (61 feet)

According to the problem, we have:
s^2 + h^2 = d^2

Substituting the given values:
11^2 + h^2 = 61^2

Simplifying:
121 + h^2 = 3721

Now, subtract 121 from both sides of the equation:
h^2 = 3721 - 121

Simplifying further:
h^2 = 3600

To find the height of the tower, we need to take the square root of both sides of the equation:
sqrt(h^2) = sqrt(3600)

Thus, the height of the tower is:
h = sqrt(3600)

Calculating the square root:
h ≈ 60 feet

Therefore, the tower is approximately 60 feet tall.

To find the height of the tower, you are correct in using the Pythagorean theorem, which states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

In this case, the length of the shadow is one of the sides, and the distance from the top of the tower to the end of the shadow is the hypotenuse. Let's call the height of the tower "h".

According to your computations:
61 squared = 11 squared + h squared
3721 = 121 + h squared
Subtracting 121 from both sides:
3721 - 121 = h squared
3600 = h squared

At this point, to find the value of "h," you need to take the square root of both sides of the equation. This cancels out the square on the right side, giving you the value of "h."

Taking the square root of 3600:
√(3600) = √(h squared)

The square root of 3600 is 60, so:
60 = h

Therefore, the height of the tower is 60 feet.