Question

find the measure of ∠j, the smallest angle in a triangle with sides measuring 11, 13, and 19. round to the nearest whole degree. 30° 34° 42° 47° law of cosines: ( a^2 = b^2 + c^2 - 2bccos(a) )

Explanation:

Step1: Recall the rule of the smallest angle

In a triangle, the smallest angle is opposite the shortest side. Here, the side opposite \(\angle J\) is \(LK = 11\). Let \(a = 11\), \(b = 13\), \(c = 19\).

Step2: Apply the Law of Cosines

The Law of Cosines formula is \(a^{2}=b^{2}+c^{2}-2bc\cos(A)\). Substituting the values:

$$
LATEXBLOCK0
$$

Step3: Find the angle

\(J=\cos^{-1}(0.828)\approx34^{\circ}\)

Answer:

\(34^{\circ}\)