Final answer:
In triangle GHJ, the value of angle ∠H is approximately 53.13°. In order to determine the angle ∠H in triangle GHJ, the Law of Cosines proves instrumental. So, the option a is correct.
Step-by-step explanation:
In order to determine the angle ∠H in triangle GHJ, the Law of Cosines proves instrumental.
This mathematical principle asserts that, within a triangle, the square of one side equals the sum of the squares of the other two sides, diminished by twice the product of those two sides and the cosine of the included angle.
In this scenario, with GH measuring 21 inches, HJ at 24 inches, and GJ spanning 9 inches, applying the Law of Cosines allows the calculation of the cosine of ∠H.
By utilizing the inverse cosine function, the value of ∠H in degrees is derived.
Upon computation, it is established that ∠H approximates 53.13°.
This analytical approach offers a precise means of ascertaining the angle within triangle GHJ based on the given side lengths, employing trigonometric principles for a comprehensive geometric analysis.
Hence, the option a is correct, in triangle GHJ, the value of angle ∠H is approximately 53.13°.