Question

Triangle J K L is shown. The length of J K is 13, the length of K L is 11, and the length of L J is 19.

Law of cosines: a2 = b2 + c2 – 2bccos(A)

Find the measure of AngleJ, the smallest angle in a triangle with sides measuring 11, 13, and 19. Round to the nearest whole degree.

30°
34°
42°
47°

Answer 1

To find the measure of Angle J, the smallest angle in triangle JKL, we can use the Law of Cosines:

a^2 = b^2 + c^2 - 2bc*cos(A)

Since angle J is opposite to side KL, we have:

a = KL = 11
b = LJ = 19
c = JK = 13

Plugging in these values, we get:

(11)^2 = (19)^2 + (13)^2 - 2(19)(13)*cos(J)

Simplifying:

121 = 361 + 169 - 494*cos(J)

-409 = -494*cos(J)

cos(J) = 409/494

Taking the inverse cosine of both sides, we get:

J = cos^-1(409/494) ≈ 34.4 degrees

Therefore, the measure of Angle J, rounded to the nearest whole degree, is 34 degrees. So the answer is option B: 34°.