Question

PLEASE HELP! Find all solutions for the triangle with f = 15, e = 14, F = 33°. If no solutions exist, write none. Round to the nearest tenth.

Answer 1

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

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Keywords : solutions, triangle, nearest tenth

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