you are standing 12ft from a cylindrical corn syrup tank the distance from you to a point of tangency on the tank 35ft what is the radius of the tank

Draw a diagram.

The line from you to the center is 12+r
The line from the center to the tangency is r, and is perpendicular.
The line from you to the tangency is 35

(r+12)^2 + r^2 = 35^2

just solve that for r.

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To find the radius of the tank, we can create a right triangle using the given information. Here's how you can do it:

1. Draw a diagram to help visualize the problem. Draw a line segment to represent the distance from you to the point of tangency, which is 35ft. Draw another line from the point of tangency to the center of the tank, creating a right angle.

2. Label the line from you to the point of tangency as the hypotenuse of the triangle. This length is given as 35ft.

3. Label the distance from the center of the tank to the point of tangency as the radius of the tank. Let's call it 'r', which is what we want to find.

4. Label the distance from you to the center of the tank as the adjacent side of the triangle. This length is 12ft.

5. Apply the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the lengths of the other two sides (a and b). In this case, a = 12ft, b = r.

So, we have: (12ft)^2 + r^2 = (35ft)^2.

6. Simplify the equation by calculating the squares: 144 + r^2 = 1225.

7. Subtract 144 from both sides to isolate r^2: r^2 = 1225 - 144.

8. Perform the subtraction: r^2 = 1081.

9. Take the square root of both sides to solve for r: r = √1081.

10. Use a calculator to find the square root of 1081: r ≈ 32.85.

Therefore, the radius of the cylindrical corn syrup tank is approximately 32.85 feet.