How do you determine whether triangle ABC has no, one, or two solutions given A=34^circ, a=8, b=13?

1 Answer
Nov 21, 2017

2 triangles.

Explanation:

If

a > b

then one triangle is formed, but if

a < b

then proceed to the formula

a " < = > " bsin(A)

In which

  • > " will yield to 2 triangles"
  • < " will yield to no triangles"
  • = " will yield to 1 right triangle"

So in the problem

8 " <=>" 13sin(34)

8>7.27

Therefore, two triangles will be formed.

Or you could use the other way (sin law)

a/sin(A)=b/sin(B)

8/sin(34)=13/sin(x)

8sin(x)=13sin(34)

sin(x)=(13sin(34))/8

x=sin^-1((13sin(34))/8)

triangle1=65.32
triangle2=180-65.32=114.68

Proving

65.32+34<180 sqrt
114.68+34<180 sqrt