ANSWER
K=43° to the nearest degree
EXPLANATION
Use the sine rule:
[tex] \frac{ \sin(J) }{j} = \frac{ \sin(L)}{l} [/tex]
Substitute the values
[tex] \frac{ \sin(J) }{10} = \frac{ \sin(102 \degree)}{17} [/tex]
This gives us,
[tex] \sin(J) = \frac{ \sin(102 \degree)}{17} \times 10[/tex]
[tex] J = \sin ^{ - 1} (0.57538094161) = 35.126 \degree[/tex]
J is approximately 35°
We now use the sum of interior angles of a triangle to find K.
[tex]K + 35 \degree + 102 \degree = 180 \degree[/tex]
[tex]K = 180 \degree - 35 \degree - 102 \degree[/tex]
[tex]K = 43 \degree [/tex]
