Law of sines: How many distinct triangles can be formed for which m∠A = 75°, a = 2, and b = 3? No triangles can be formed. One triangle can be formed where angle B is about 15°. One triangle can be formed where angle B is about 40°. Two triangles can be formed where angle B is 40° or 140°.

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ApusApus ApusApus · Answer 1 · 2018-09-10T17:06:18+02:00

We have been given angle A as 75 degrees and sides a = 2 and b = 3.

Using Sine rule, we can set up:

[tex]\frac{Sin(A)}{a}=\frac{Sin(B)}{b}[/tex]

Upon substituting the given values of angle A, and sides a and b, we get:

[tex]\frac{Sin(75)}{2}=\frac{Sin(B)}{3}[/tex]

Upon solving this equation for B, we get:

[tex]\Rightarrow 3Sin(75)=2Sin(B)\\ \Rightarrow Sin(B)=\frac{3Sin(75)}{2}\\ \Rightarrow Sin(B)=1.4488\\[/tex]

Since we know that value of Sine cannot be more than 1. Hence there are no values possible for B.

Hence, the triangle is not possible. Therefore, first choice is correct.

ashishdwivedilVT ashishdwivedilVT · Answer 2 · 2022-03-22T10:05:47+01:00

No triangles can be formed since the value of Sin B is more than 1.

It is given that

In a triangle ABC

a=2

b=3

∠A =75°

Sine rule states that in a triangle ABC with usual notations of sides a,b and c,

[tex]\frac{SinA}{a} =\frac{SinB}{b} =\frac{SinC}{c}[/tex]

From sine rule,

[tex]\frac{Sin75}{2} = \frac{SinB}{3}[/tex]

Sin B = 1.45 (Not possible)

Since we know that the range of sine function is [-1,1], no values of ∠B are possible. So, no triangle can be formed.

Therefore, No triangles can be formed since the value of Sin B is more than 1.

To get more about the sine rule visit:

https://brainly.com/question/309896