The smallest angle occurs opposite the shortest side length of the triangle. So by the law of cosines we have
[tex]11^2=13^3+19^2-2\cdot13\cdot19\cos\angle J\implies\cos\angle J=\dfrac{409}{494}\implies\theta\approx\boxed{34^\circ}[/tex]
Answer:
The measure of angle J is 34°
Step-by-step explanation:
Given,
J is the smallest angle in the triangle with sides measuring 11, 13, and 19,
Thus, J must be the opposite angle of the side measuring 11,
Since, the law of cosines,
[tex]a^2 = b^2 + c^2 - 2bc cos A[/tex]
Where, a, b and c are the sides of a triangle ABC,
Such that angle A is opposite to the side measuring a,
By applying the law,
We can write,
[tex]11^2 = 13^2 + 19^2 - 2\times 13\times 19 cos J[/tex]
[tex]121 = 169 + 361 - 494 cos J[/tex]
[tex]\implies cos J = \frac{169+361-121}{494}=\frac{409}{494}[/tex]
[tex]\implies m\angle J=34.1127839945\approx 34^{\circ}[/tex]
Second option is correct.
