Respuesta :

I tried Law of Sines but remembered, that only determines even if you HAVE a triangle.

But still, you'll know if you have NO solution or at least a solution.

Here, by applying the Law of Sines...

sin(42°)/92 = sin(B)/120

92sin(B) = 80.295
sin(B)=0.873
B=60.78°

We know that this has at LEAST one solution now.

I've attached the formula instance when there's two triangles/solutions, or what we call the Ambiguous Case.

But I've also attached a picture of the one triangle case: two ways it could have one triangle for a solution.

Clearly, 92 is not bigger than 120 and since angle B is equal to 60.78 degrees, a does not equal h.

Well, now we know two triangles can be formed, and if you verify, yup.
Ver imagen Аноним

The number of triangles that can be formed is one

Data;

  • b = 120
  • c = 92
  • C = 42°
  • B = ?

Sine Rule

We can use sine rule to find the length of the missing side

This is given as

[tex]\frac{b}{sinB} = \frac{c}{sinC} \\[/tex]

Let's substitute the values and solve.

[tex]\frac{b}{sinB} = \frac{c}{sinC} \\\frac{120}{sinB}= \frac{92}{sin42} \\ sinB = \frac{120 * sin42}{92} \\sinB = 0.87278\\B = sin^-^1 0.87278\\B = 60.78^0[/tex]

But with any given triangle, we should have 3 sides and 3 angles.

The number of triangles that can be formed is one

Learn more on sine rule here;

https://brainly.com/question/8823652

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