Question

calculator
what is the measure of ∠j to the nearest degree?
45°
55°
70°
83°

Explanation:

Step1: Apply Law of Sines

$\frac{\sin(\angle J)}{GH} = \frac{\sin(\angle G)}{JH}$

Step2: Substitute known values

$\frac{\sin(\angle J)}{5} = \frac{\sin(80^\circ)}{7}$

Step3: Isolate $\sin(\angle J)$

$\sin(\angle J) = \frac{5 \times \sin(80^\circ)}{7}$

Step4: Calculate the value

$\sin(\angle J) \approx \frac{5 \times 0.9848}{7} \approx 0.7034$

Step5: Find $\angle J$ via arcsine

$\angle J \approx \arcsin(0.7034) \approx 45^\circ$

Answer:

45°