Question

Determine the distance (D) between the bends of a compound 90° bend using 45° bends that are installed to avoid a rectangular obstruction where the short side of the rectangle (SR) is 6 inches and the long side of the rectangle (LR) is 21 inches. (Round your FINAL answer to the nearest tenth or one decimal place.)

Answer 1

The distance (D) between the bends to avoid a rectangle with sides 6 and 21 inches is approximately 21.8 inches, calculated using the Pythagorean theorem.

Step-by-step explanation:

To determine the distance (D) between the bends of a compound 90° bend using 45° bends installed to avoid a rectangular obstruction, we need to calculate the diagonal of the rectangle formed by the short side (SR) and the long side (LR). The SR is given as 6 inches, and the LR is 21 inches.

The diagonal D can be found using the Pythagorean theorem: D = √(SR² + LR²). Plugging in the values, we have D = √(6² + 21²), which simplifies to D = √(36 + 441) or D = √477. Calculating this, we find that D ≈ 21.8 inches (rounded to the nearest tenth).

Therefore, the distance between the bends is approximately 21.8 inches.

Answer 2

To calculate the distance (D) between the compound bends, we use the Pythagorean theorem on one of the right-angled triangles formed by the bend around the obstruction; then, we double the hypotenuse to get the total distance. In this case, the distance is approximately 43.6 inches.

Step-by-step explanation:

To find the distance (D) between the bends of a compound 90° bend using 45° bends to avoid a rectangular obstruction, we can visualize the setup as two right-angled triangles back-to-back. Each triangle will have legs corresponding to the short side (SR) and the long side (LR) of the obstruction. Since SR is 6 inches and LR is 21 inches, we can use the Pythagorean theorem to calculate the hypotenuse of one triangle, which is half of the total distance D needed.

We calculate the hypotenuse (h) of one triangle as:
h = √(SR² + LR²) = √(6² + 21²) = √(36 + 441) = √477

Now, multiplying the hypotenuse of one triangle by 2 to get the combined length for both right-angled triangles that form the compound bend:
D = 2 × h = 2 × √477
When we calculate this, we obtain:

D = 2 × 21.8 (rounded to one decimal place) ≈ 43.6 inches