The measure of angle J is 19.8°, and the correct option is D.
The law of cosine or cosine rule in trigonometry is a relation between the side and the angles of a triangle. Suppose a triangle with sides a, b, c and with angles cosC.
The following formula is used to find the angle j is;
[tex]\rm j^2 = h^2 + i^2 -2hicosC[/tex]
Triangle HIJ has side lengths h=12, i = 17, j = 7.
Substitute all the values in the formula;
[tex]\rm j^2 = h^2 + i^2 -2hicosJ\\\\(7)^2=(12)^2+(17)^2-2 \times 12 \times 17 cosJ\\\\49=144+289-408cosJ\\\\144+289 -49 =408cosJ\\\\384 =408cosJ\\\\cosJ=\dfrac{384}{408}\\\\cosj = 0.94\\\\J =cos^{-1}(0.94)\\\\J=19.8[/tex]
Hence, the measure of angle J is 19.8°, and the correct option is D.
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