Find the length of the side of the largest square nut that can be milled from a piece of round stock that the diameter is 15mm. Use the 45-45-90 degree formula to solve.

Why did the nut go to the gym? Because it wanted to get "squared" muscles, of course! Now, let's bring out our trusty 45-45-90 degree formula to solve this nutty problem.

In a 45-45-90 degree triangle, the length of the hypotenuse (c) is equal to the side length (s) multiplied by the square root of 2 (√2). So, for our square nut, the hypotenuse is going to be the diameter of the stock, which is 15mm.

Let's call the side length of the square nut "s". According to the formula, we can set up the equation:

s√2 = 15mm

To solve for "s", we can divide both sides of the equation by √2:

s = 15mm / √2

Calculating this out, we get approximately:

s ≈ 10.61mm

So, the length of the side of the largest square nut that can be milled from the round stock with a diameter of 15mm is about 10.61mm. Happy nut-milling!

To find the length of the side of the largest square nut that can be milled from a piece of round stock with a diameter of 15mm, we can use the 45-45-90 degree formula.

In a 45-45-90 triangle, the lengths of the sides are in a ratio of 1:1:√2.

Since the square nut will have sides of equal length, we need to find the length of one of the sides.

The diagonal of the square nut will be the diameter of the round stock, which is 15mm.

In a 45-45-90 triangle, the length of the hypotenuse (diagonal) is √2 times the length of one of the legs (side).

We can set up an equation to find the length of one side:

Length of one side = (Diameter of round stock) / √2

Length of one side = 15mm / √2

To simplify this, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of √2, which is also √2:

Length of one side = (15mm / √2) * (√2 / √2)

Length of one side = 15√2 mm / 2

Length of one side = (15/2)√2 mm

Therefore, the length of the side of the largest square nut that can be milled from the round stock with a diameter of 15mm is (15/2)√2 mm.

To find the length of the side of the largest square nut that can be milled from a piece of round stock, we can start by using the 45-45-90 degree formula.

The 45-45-90 degree formula states that in a right triangle where two of the angles are 45 degrees, and the sides opposite those angles are equal, the ratio of the side lengths is 1:1:√2.

In this case, we want to find the length of the side of the square nut, which is our hypotenuse, given that the other two sides are equal.

Since the diameter of the round stock is 15mm, the radius (half the diameter) is 15/2 = 7.5mm.

In a square nut, the diagonal (hypotenuse) is equal to twice the length of the side, so we can write the equation as:

2s = diagonal

Using the 45-45-90 degree formula, we know that the ratio of the diagonal to the side of the square nut is √2:1.

Therefore, we can write the equation as:

√2s = diagonal

Substituting the value of the radius for the diagonal, we have:

√2s = 7.5mm

To solve for s, we divide both sides of the equation by √2:

s = 7.5mm / √2

To simplify the expression, we can multiply the numerator and denominator by √2:

s = (7.5mm * √2) / (√2 * √2)
s = 7.5mm√2 / 2

Now, we can simplify further by rationalizing the denominator:

s = (7.5mm√2 / 2) * (√2 / √2)
s = (7.5mm * 2) / 2√2
s = 15mm / 2√2

Finally, we simplify the expression by multiplying the numerator and denominator by the conjugate of the denominator:

s = (15mm / 2√2) * (√2 / √2)
s = (15mm√2) / (2 * √2 * √2)
s = (15mm√2) / (2 * 2)
s = (15mm√2) / 4

Therefore, the length of the side of the largest square nut that can be milled from a piece of round stock with a diameter of 15mm is (15mm√2) / 4.