B. g=24.6,E=30.6°,G=116.4°
Step-by-step explanation:
In this question apply the sine law which is written as;
a/sin A = b/sin B = c/sin C where a,b,c are sides and A is the angle opposite to side a, B is the angle opposite to side b, and C is the angle opposite to side c.
In this case, e/sin E = f/sin F = g/ sin G
Given that f=15, e=14 and F=33° then ;
1. Finding angle ∠E will be;
f/sin F = e/sin E
15/sin 33° =14/sin E
27.5 =14/sin E
sin E= 14/27.50
sin E=0.5083297660
E= sin⁻(0.5083297660)
∠E=30.6°
2.
Finding angle G where sum of angles in a triangle add up to 180° then;
∠G = 180°-(30.6°+33°)
∠G=180°-63.6° = 116.4°
3.
Finding side g will be;
g/sinG =f/sinF
g/sin G = 15/sin F
g/sin 116.4°=15/sin 33°
g/116.4° = 27.50
g= 27.50 sin 116.4°
g=24.6
Learn More
Sine Law :https://brainly.com/question/12520380
Keywords : solutions, triangle, nearest tenth
#LearnwithBrainly
