Question

solve for x. round your answer to the nearest tenth if necessary. figures are not necessarily drawn to scale.

Explanation:

Step1: Find the third angle of triangle \(KIJ\)

The sum of angles in a triangle is \(180^{\circ}\). Let the third angle of \(\triangle KIJ\) be \(A\). Then \(A = 180-(74 + 54)=52^{\circ}\)

Step2: Use the Law of Sines

For \(\triangle KIJ\), by the Law of Sines \(\frac{14}{\sin52^{\circ}}=\frac{13}{\sin54^{\circ}}\) (not relevant for our final proportion). For \(\triangle MNL\) and \(\triangle KIJ\) (since angles \(52^{\circ},54^{\circ}\) and the third - angle relationship, the triangles are similar).
By the Law of Sines (for similar triangles, the ratio of corresponding sides is equal). \(\frac{x}{14}=\frac{19}{13}\)

Step3: Solve for \(x\)

Cross - multiply: \(13x=19\times14\). Then \(x=\frac{19\times14}{13}=\frac{266}{13}\approx20.5\)

Answer:

\(x\approx20.5\)