Final answer:
To find the length of side i in triangle IJK, we use the Law of Cosines.
Step-by-step explanation:
To find the length of side i in triangle IJK, we can use the Law of Cosines.
The Law of Cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the magnitudes of those sides multiplied by the cosine of the included angle. In this case, we have: i^2 = j^2 + k^2 - 2 * j * k * cos(I).
Plugging in the given values, we get: i^2 = (820^2) + (400^2) - 2 * 820 * 400 * cos(55).
Solving for i, we take the square root of both sides: i = sqrt((820^2) + (400^2) - 2 * 820 * 400 * cos(55)). Using a calculator, we find that i ≈ 724.47 inches.
Rounding to the nearest inch, the length of side i is 724 inches.