In ΔHIJ, j = 72 cm, i = 70 cm and ∠I=72°. Find all possible values of ∠J, to the nearest degree.

To solve this problem, we will 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 the side of length c, the following equation holds:

c² = a² + b² - 2ab cos(γ)

In this case, we have a triangle ΔHIJ with sides h = 70 cm, i = 72 cm, and j = 72 cm, and an angle I = 72° opposite the side of length i. We want to find the angle J, which is opposite the side of length j. We can rearrange the Law of Cosines to solve for cos(J):

cos(J) = (h² + i² - j²) / (2hi)

Substituting the given values:

cos(J) = (70² + 72² - 72²) / (2 * 70 * 72) cos(J) = (4900 + 5184 - 5184) / (10080) cos(J) = 4900 / 10080 cos(J) = 0.48611

Now we can find the angle J by taking the arccosine of cos(J):

J = arccos(0.48611) J = 61° (to the nearest degree)

So, the possible value for ∠J is 61°.