Question

How many triangles can be formed if in triangle ABC, b=120, c=92 and C=42°?

Answer 1

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.

Answer 2

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

$\frac{b}{sinB} = \frac{c}{sinC}$

Let's substitute the values and solve.

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

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