Question

Solve the triangle. A = 51°, b = 14, c = 6a. No triangles possibleb. a ≈ 14.9, C ≈ 28.1, B ≈ 100.9c. a ≈ 11.2, C ≈ 24.1, B ≈ 104.9d. a ≈ 14.9, C ≈ 24.1, B ≈ 104.9

Answer 1

we have that
A = 51°, b = 14, c = 6

step 1
find the value of a
Applying the law of cosines
a²=c²+b²-2*c*b*cos A
a²=6²+14²-2*6*14*cos 51-------> 126.27
a=11.2

we know that

The sum of the lengths of any two sides of a triangle is greater than the length of the third side. (Triangle Inequality Theorem)

we have

a=11.2

b=14

c=6

so

(a+b) > c-------------> (11.2+14)=25.2

25.2 > 6-----> is not correct

therefore

the answer is the option

a. No triangles possible