Question

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°.

Answer 1

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

Using Sine rule, we can set up:

$\frac{Sin(A)}{a}=\frac{Sin(B)}{b}$

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

$\frac{Sin(75)}{2}=\frac{Sin(B)}{3}$

Upon solving this equation for B, we get:

$\Rightarrow 3Sin(75)=2Sin(B)\\ \Rightarrow Sin(B)=\frac{3Sin(75)}{2}\\ \Rightarrow Sin(B)=1.4488$

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.

Answer 2

No triangles can be formed is the right answer!