Final answer:
Using the Law of Cosines with the given side lengths, we calculate the measure of angle J in triangle JKI to be approximately 14° to the nearest degree.
Step-by-step explanation:
To find the measure of ∠ J in triangle JKI with sides
j=74 cm,
k=14 cm, and
l=80 cm,
we can use the Law of Cosines. The Law of Cosines states that for any triangle with sides a, b, and c and opposite angles A, B, and C respectively: c² = a² + b² - 2ab×cos(C).
In our case, we are looking for angle J, so we will rearrange the formula to solve for cos(J): cos(J) = (j² + l² - k²)/(2×j×l).
Substituting the given values:
cos(J) = (74² + 80² - 14²)/(2×74×80)
= (5476 + 6400 - 196)/(2×14800)
= (11680 - 196)/(2×74×80)
= 11484/11840
= 0.96949153
∠ J = cos⁻¹(0.96949153) ≈ cos⁻¹(0.9695) ≈ 14° (to the nearest degree, using a calculator with inverse cosine function).
Therefore, the measure of ∠ J is approximately 14°.