In ΔIJK, j = 530 cm, i = 740 cm and ∠I=133°. Find all possible values of ∠J, to the nearest degree.

To find the possible values of ∠J in ΔIJK, we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides of lengths a, b, and c and an angle γ opposite side c, the following relationship holds:

c² = a² + b² - 2ab cos(γ)

In this case, we know that side i = 740 cm, side j = 530 cm, and ∠I = 133°. We want to find ∠J, which is the angle opposite side j. So we can rearrange the Law of Cosines to solve for cos(γ):

cos(γ) = (a² + b² - c²) / (2ab)

Substituting the given values:

cos(J) = (i² + k² - j²) / (2ik) cos(J) = ((740)² + k² - (530)²) / (2 * 740 * k)

We don't know the length of side k, so we can't solve for cos(J) directly. However, we know that -1 ≤ cos(J) ≤ 1, so we can find the range of possible values for ∠J.

If cos(J) = -1, then J = 180°. If cos(J) = 1, then J = 0°.

So the possible values of ∠J are 0° ≤ J ≤ 180°. However, we know that the sum of the angles in a triangle is 180°, and we already have ∠I = 133°. So the maximum possible value for ∠J is 180° - 133° = 47°.

Therefore, the possible values of ∠J, to the nearest degree, are 0° ≤ J ≤ 47°.