State whether the given measurements determine zero, one, or two triangles. B = 86°, b = 21, c = 18

1 answer:

8 0

We know that
Applying the law of sines
b/sin B=c/sin C-----> b*sin C=c*sin B-----> sin C=c*sin B/b
c=18
b=21
B=86°
sin C=18*sin 86/21-----> sin C=0.8550------> C=arc sin(0.8550)
C=58.77°------> C=58.8°
calculate angle A
A+B+C=180--------> A=180-B-C----> A=180-86-58.8----> A=35.2°
b/sin B=a/sin A-------> a=b*sin A/sin B----> a=21*sin 35.2/sin 86
a=12.13-------> a=12

the measure of the first triangle are
a=12
b=21
c=18
A=35.2°
B=86°
C=58.8°

calculate the measures of the second triangle
b=21
c=18
B=86°
C=180-58.8----> C=121.2°
A+B+C=180-----> A=180-86-121.2----> A=-27.2----> It is not possible to build a second triangle

the answer is
it is possible to assemble only a single triangle
a=12
b=21
c=18
A=35.2°
B=86°
C=58.8°

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