Question

what is the approximate perimeter of the triangle? use the law of sines to find the answer. law of sines: $\frac{sin(a)}{a}=\frac{sin(b)}{b}=\frac{sin(c)}{c}$

Explanation:

Step1: Find angle J

The sum of angles in a triangle is 180°. So, $\angle J=180^{\circ}-(67^{\circ} + 74^{\circ})=39^{\circ}$.

Step2: Use law of sines to find side JK

By the law of sines $\frac{\sin(J)}{KL}=\frac{\sin(L)}{JK}$. Substituting the values, $\frac{\sin(39^{\circ})}{2.3}=\frac{\sin(74^{\circ})}{JK}$. Then $JK=\frac{2.3\times\sin(74^{\circ})}{\sin(39^{\circ})}\approx\frac{2.3\times0.9613}{0.6293}\approx3.5$.

Step3: Use law of sines to find side JL

Using the law of sines $\frac{\sin(J)}{KL}=\frac{\sin(K)}{JL}$. Substituting values, $\frac{\sin(39^{\circ})}{2.3}=\frac{\sin(67^{\circ})}{JL}$. Then $JL=\frac{2.3\times\sin(67^{\circ})}{\sin(39^{\circ})}\approx\frac{2.3\times0.9205}{0.6293}\approx3.4$.

Step4: Calculate the perimeter

Perimeter $P = JK + JL+KL$. So $P\approx3.5 + 3.4+2.3 = 9.2$ units.

Answer:

9.2 units