Question

What is the approximate length of ? Use the law of sines to find the answer.

Answer 1

Sine (Angle K) / side k = sine (105) / 4.7
Sine Angle K  = (2.7 * 0.96593) / 4.7
Sine Angle K =  0.5548959574
Angle K = 33.704 degrees
Angle J = 180 -105 -33.704 = 41.296
Sine J / side (j) = sine (105) / 4.7
Sine (41.296) / side (j) = 0.96593 / 4.7
Side (j) = Sine (41.296) / 0.96593 / 4.7
Side (j) = 0.65995 / 0.2055170213
Side (j) = 3.21117

Answer 2

Answer: Third option is correct.

Step-by-step explanation:

Since we have given that

JL = 2.7 units

JK = 4.7 units

∠L = 150°

Using Law of sines,

$\frac{\sin L}{L}=\frac{\sin K}{K}=\frac{\sin J}{J}\\\frac{\sin 105^\circ}{4.7}=\frac{\sin K}{2.7}\\\\\frac{\sin 105^\circ\times 2.7}{4.7}=\sin K\\\\0.5548=\sin K\\\\\sin^{-1}(0.5548)=K\\\\33.7^\circ=K$

Now, using "Sum of interior angles of a triangle is supplementary."

$\angle J+\angle K+\angle L=180^\circ\\\\\angle J+33.7^\circ+105^\circ=180^\circ\\\\\angle J+138.7^\circ=180^\circ\\\\\angle J=180^\circ-138.7^\circ\\\\\angle J=41.3^\circ$

Again by using "Law of sines" we get,

$\frac{\sin L}{L}=\frac{\sin K}{K}=\frac{\sin J}{J}\\\\\frac{\sin 105^\circ}{4.7}=\frac{\sin 41.3^\circ}{J}\\\\J=\frac{\sin 41.3^\circ \times 4.7}{\sin 105^\circ}\\\\J=3.211\\\\J=3.2\ approx.$

Hence, Third option is correct.